arrow right. It can factor expressions with polynomials involving any number of vaiables as well as more complex functions.200 x = 2 Step by step solution : Step 1 :Equation at the end of step 1 : (5x2 - 11x) + 2 = 0 Step 2 :Trying to (x-4)(3x+1) To factor this quadratic, you need a generic rectangle and a diamond problem First, we need to find the sum and product of the diamond problem. Factor by grouping. Solve. 2)Product of zeros= … x^2+2x+1=3x-10; 2x^2+4x-6=0; Show More; Description. On the last post we covered completing the square (see link).1 Factoring x2+11x-210 The first term is, x2 Verified answer. Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator. 3x2 − 11x − 20 3 x 2 - 11 x - 20. verified. Hence the positive x-intercept is (4, 0) Learn more on Middle School Math Solutions - Polynomials Calculator, Factoring Quadratics. Step 3. Open in App. heart. Get the x-intercepts. -x^2-3x+4 C. 3x^2-11x - 4=0 .1 Factoring 3x2-11x+30. 5/5. →3x^2 +12x-x-4=0. The sum of the diamond problem is -11x. 2 2 3 4. Tap for more steps 3x2 + 4x−15x−20 3 x 2 + 4 x - 15 x - 20. I'm seeing a -4 at the end of the equation. Step 1. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. 3x² − 11x + 14x=0. verified. X^4-11x^2+28 B. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a Substitute the values a = 3 a = 3, b = −11 b = - 11, and c = −4 c = - 4 into the quadratic formula and solve for x x. The middle term is, -11x its coefficient is -11 . In other words, we are going to solve as many equations as there are terms in the product. messages. $$ \left( x^{4} + x^{3} - 9 x^{2} + 11 x - 4 \right) $$ x2-11x+24=0 Two solutions were found : x = 8 x = 3 Step by step solution : Step 1 :Trying to factor by splitting the middle term 1. This is the same as solving: (x-4) (3x+1)=0 (because this is just the factored form of the original equation.333 Solve : x+4 = 0 Subtract 4 from both 3 { x }^{ 2 } -11x-4. heart outlined. Earlier we factored this polynomial by splitting the middle term. Expert-Verified Answer %counter% people found it helpful. 1)sum of zeros = 1/3-4= -11/4 = -b/a . Frequently Asked Questions (FAQ) What are the solutions to the equation 5x^2-11x+4=0 ? 3x2-11x-874=0 Two solutions were found : x = -46/3 = -15. x = 4.1 Factoring x2-11x+24 The first term is, x2 its 5x2-11x+2=0 Two solutions were found : x = 1/5 = 0. 3x^{2}-11x+4=0 . Tap for more steps x2 + 11x 3 = 4 3.333. View Solution. Parabola, Finding the Vertex : 4. Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator. What are the possible rational roots of #6x^4+35x^3-x^2-7x-1=0# and then determine the rational roots? =36x^4-12x^3-11x^2+2x+1#? How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=3x^3+3x^2-11x-10#? Get Step by Step Now. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C.1. x−3 = 0 x - 3 = 0. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. Send us Feedback. To solve the equation for different variables step-by-step clear any fractions by multiplying both sides of the equation by the LCM of the denominators. Solve 3x^2+11x-4 | Microsoft Math Solver Solve Factor Solution Steps Steps Using the Quadratic Formula Steps Using Direct Factoring Method View solution steps Evaluate … Solving 3x 2 +11x-4 = 0 directly . -11/3 b. 3x^2-11x-4=0 3. Step 3. 1: 2: 3: 4: 5: 6: 7: 8: 9: 0. Penyelesaian dari 3x^2 -11x - 4 = 0adalah a dan b. →3x^2 +12x-x-4=0. The first term is, 3x2 its coefficient is 3 . View Solution.2. Share. Tap for more steps The value of ( 1 5) + [ 1 1 4 − 1 2] × ( 2 5) lies between: Q2. . In this case, the divisor is x −2 so we have to change −2 to 2., < > ≤: ≥ ^ √: ⬅: : F _ ÷ | (* / ⌫ A: ↻: x: y = +-G Byju's Answer Standard VIII Mathematics Factorisation of Trinomial Factorise 3x^ Question Factorise: 3 x 2 + 11 x - 4 = 0 Solution Factorization The given equation is, . a+b=-11 ab=3\left(-4\right)=-12 . Just like numbers have factors (2×3=6), expressions have factors ( (x+2) (x+3)=x^2+5x+6). Penyelesaian Persamaan Kuadrat. Subtract 4/3 from both side of the equation : x2+ (11/3)x = -4/3. Study with Quizlet and memorize flashcards containing terms like Using the quadratic equation to solve 3x 2 + 11x - 4 = 0, the value of b 2 - 4ac is, Solve the following problem for the roots by using the quadratic formula. Save to Notebook! Sign in.1. 3X^{2}+11X-20=0. let us now solve the equation by Completing The Square and by using the Quadratic Formula. heart. View Solution. →3x(x+4)-1(x+4)=0. Copied to clipboard. Solve for x 3x+2=11. PERSAMAAN KUADRAT. Weegy: 3x + 5 -6/-3 x > 2 (More) 2. Step-by-step explanation: A. Use the quadratic formula to find the solutions. Q4. Factor using the rational roots test. Isolate the variable, and solve for the variable by undoing any arithmetic Free quadratic equation factoring calculator - Solve quadratic equations using factoring step-by-step. Copied to clipboard.) 3x^2 - 11x - 4 = 0 Step-by-step explanation: Click an Item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. In order to complete the square, the equation must first be in the form x^{2}+bx=c. The Factoring Calculator transforms complex expressions into a product of simpler factors.1 Find the Vertex of y = 3x 2-11x-4 3.9 + 0. Factorize the result to have: 3x² -12x + x - 4 = 0 Factor out the GCF. Factoring is the process Read More.5. Factoring is the process Read More. 6. Q4. star. or , x+4=0. View Solution. Penyelesaian Persamaan Kuadrat. 3x + 2 = 11 3 x + 2 = 11. Tap for more steps 3x2 + x−12x−4 3 x 2 + x - 12 x - 4 Steps Using Direct Factoring Method View solution steps Graph Graph Both Sides in 2D Graph in 2D Quiz Quadratic Equation 3x2 −11x+4 = 0 Similar Problems from Web Search −3x2 − 11x + 4 = 0 Online math solver with free step by step solutions to algebra, calculus, and other math problems. Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula.)6+x5+2^x=)3+x( )2+x( ( srotcaf evah snoisserpxe ,)6=3×2( srotcaf evah srebmun ekil tsuJ . Q3. Solve 3x^2+11x-4 | Microsoft Math Solver Solve Factor Solution Steps Steps Using the Quadratic Formula Steps Using Direct Factoring Method View solution steps Evaluate Graph Quiz Polynomial 5 problems similar to: Share Examples Quadratic equation Trigonometry Linear equation Arithmetic Matrix Simultaneous equation Differentiation Integration Solving 3x 2 +11x-4 = 0 directly . Earlier we factored this polynomial by splitting the middle term. 3x4 − 11x3 − x2 +19x+6 = 0 3 x 4 - 11 x 3 - x 2 + 19 x + 6 = 0. Get two numbers when you multiply them it will give you 24 but if you add them it will give 11.8) × 0. Step 2: Change the sign of a number in the divisor and write it on the left side. . This answer has been confirmed as correct and helpful. Multiply by .369 x = (-11+√161)/10= 0.956 x = (13+√509)/10= 3. The marked price is 10% higher than cost price. This answer has been confirmed as correct and helpful. heart outlined. x ^ 2 -\frac{11}{3}x -\frac{4}{3} = 0. If 3x2 - 11x - 4 = (3x + 1)(x - 4), which equations should be solved to find the roots of 3x2 - 11x - 4 = 0? star. →x=1/3 or , -4 .003234 to scientific ; 1, 7, 13 Precalculus. If Jonathan is twice as old as his 3x2+11x-25=0 Two solutions were found : x = (-11-√421)/6=-5. Not sure where -12 came from. 11/3 d.110 Step by step solution : Step 1 :Trying to factor by splitting the middle term 1. 5/5. The numbers are +8 and +3 because +8 x +3= +24. Therefore, Similar Questions. 3X^{2}+11X-20=0. The first term is, 3x2 its coefficient is 3 . Save to Notebook! Sign in. quadratic-equation-calculator. or , x+4=0. Algebra. By splitting the middle term. According to the Quadratic Formula, x , the solution for Ax 2 +Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by : How do you solve using the completing the square method #3x^2 + 11x - 4 = 0#? Algebra Quadratic Equations and Functions Completing the Square. Parabola, Finding the Vertex : 4. y=-4-14x. First, the expression needs to be rewritten as 3x^{2}+ax+bx-4.yfilpmis dna 3 yb 4 = x11 + 2x3 ni mret hcae ediviD . 3x 2 - x + 12x - 4 = 0. Verified by Toppr.1. 3*4 = 12. 3x(x-4) + 1(x-4) = 0 (3x+1) (x-4) = 0. Thanks Find the Roots (Zeros) 2x^3-3x^2-11x+6=0. Factorize the result to have: 3x² -12x + x - 4 = 0 Factor out the GCF. Online math solver with free step by step solutions to algebra, calculus, and other math problems. The last term, "the constant", is +30. An example of a polynomial of a single indeterminate x is x² − 4x + 7.1 Find the Algebra Free math problem solver answers your algebra homework questions with step-by-step explanations. Nilai dari 9ab adalah A. x ^ 2 -\frac{11}{3}x -\frac{4}{3} = 0. For example, enter 3x+2=14 into the text box to get a step-by-step explanation of how to solve 3x+2=14.1. High School Math Solutions - Quadratic Equations Calculator, Part 1. If m and n are the zeros of the polynomial, find the value of m/n+n/m. . en. x + 4 = 0 → x = −4. Multiply the constant 4 by 6x^2. let us now solve the equation by Completing The Square and by using the Quadratic Formula. Jonathan and his sister Jennifer have a combined age of 48. a+b=11 ab=3\left(-4\right)=-12 . Related Symbolab blog posts. 176. An example with three indeterminates is x³ + 2xyz² − yz + 1. Tap for more steps Step 1.) Now this means either x-4=0 or 3x+1=0.333 x = 19 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 - 11x) - 874 = 0 Step 2 :Trying to factor by 3x2-11x-2=0 Two solutions were found : x = (11-√145)/6=-0. Hence , required zeros are -1/3 and -4 . Add 4 to both sides of the equation. Solution. mark as a brainlist. . Step 3: Carry down the leading coefficient. 3x+1=0 requires two steps. -1 B. Steps Using Direct Factoring Method.21- . →3x-1=0. Isolate the variable, and solve for the variable by undoing any arithmetic Free quadratic equation factoring calculator - Solve quadratic equations using factoring step-by-step. Move all terms not containing x x to the right side of the equation. Click here 👆 to get an answer to your question ️ The sum of the roots of 3x 2 + 11x - 4 = 0 is -11/3 -4/3 11/3 4/3 3x^2 - 11x - 4 = 0 (3x + 1)(x - 4) = 0 3x + 1 = 0; x = -1/3 x - 4 = 0; x = 4 {-1/3, 4} is the solution set of 3x^2 - 11x - 4 = 0 answer B. A quadratic equation is a second degree polynomial having the general form ax^2 + bx + c = 0, where a, b, and c Read More. Added 4/16/2015 8:05:49 PM. 9. Step 3. View solution steps. 3x2 − 11x + 6 = 0 3 x 2 - 11 x + 6 = 0. View Solution. →3x(x+4)-1(x+4)=0. Factor the left side of the equation. heart. The sum of the polynomials is simply the result of clearing the brackets, grouping like terms and simplifying the terms. Steps for Completing the Square. On the last post we covered completing the square (see link). 3X²+11X-4=0 por factorización paso a paso con comprobación por favor! Ver respuesta (3x-1)(x+4)=0 Publicidad Publicidad josesosaeric josesosaeric Tenemos que, realizando la factorización de la expresión dada por vamos a obtener como resultado . Step 1: Enter the expression you want to factor in the editor. follow me. Subtract from both sides of the equation. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -4 and q divides the leading coefficient 2.2. (3x −1)(x +4) = 0. 5. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a. Tap for more steps 4x2 − 9 = 0 4 x 2 - 9 = 0. Parabola, Finding the Vertex : 6. Tap for more steps (3x−1)(x +4) = 0 ( 3 x - 1) ( x + 4) = 0 If any individual factor on the left side of the equation is equal to 0 0, the entire expression will be equal to 0 0. 3x^{2}-11x-4=0 Quadratic equations such as this one can be solved by completing the square. Solve for x x. Set equal to . Supplement : Solving Quadratic Equation Directly Solving 3x 2-11x-4 = 0 directly . If Jonathan is twice as old as his sister, how old is Jennifer. Similar Questions. Step-2 : Find two factors of 90 whose sum equals the coefficient of the middle term, which is -11 . the sum of the root of 3x^2+11x-4=0. To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b.174 x = (11+√145)/6= 3. Tap for more steps 3x = 9 3 x = 9. heart. The sun of the roots of 3x^2+11x-4=0. Subtracting 4 from itself leaves 0. Try this example now! » More Examples Trying the examples on the Examples page is the quickest way to learn how to use the calculator. Solution. Log in for more information. 14x + y = −4. 2x2 + 1x + 6x + 3. Related Symbolab blog posts. Step 5. and +8 + 3 = 11. Popular Problems Algebra Solve by Factoring 3x^2+11x-4=0 3x2 + 11x − 4 = 0 3 x 2 + 11 x - 4 = 0 Factor by grouping. Tap for more steps Step 1.. Tap for more steps Step 1. Where: a = 1, b = −1 and c = −2. heart.

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X^2+11x+28 D. Middle School Math Solutions – Inequalities Calculator. Tap for more steps 3x2 − 2x−9x+6 3 x 2 - 2 x - 9 x + 6.333333333 Steps Using Factoring By Grouping Steps Using the Quadratic Formula Steps for Completing the Square Steps Using Direct Factoring Method View solution steps Graph Graph Both Sides in 2D Graph in 2D Quiz Polynomial 3x2 +11x−4 = 0 Similar Problems from Web Search Free quadratic equation calculator - Solve quadratic equations using factoring, complete the square and the quadratic formula step-by-step Algebra Solve Using the Quadratic Formula 3x^2-11x-4=0 3x2 − 11x − 4 = 0 3 x 2 - 11 x - 4 = 0 Use the quadratic formula to find the solutions.4. Q3. Solve : 3 x 2 + 11 x + 10 = 0. Enter a … Algebra. PERSAMAAN KUADRAT. View Solution. 3x(x+1)=0. Set 3x4 −11x3 −x2 +19x+6 3 x 4 - 11 x 3 - x 2 + 19 x + 6 equal to 0 0. Solve quadratic equations step-by-step.(2) Substitute equation (1) in (2)-4-14x= 3x² − 11x − 4. This answer has been confirmed as correct and helpful. If a, b and c are the roots of the polynomial 3x³ + 11x - 22 and sum of the roots is 0, then find the value of a³ + b³ + c³. →(3x-1)(x+4)=0. Verified answer. 3x = 1 and x = -4. Find the roots of quadratic equation √3x^2 + 11x + 6√3 = 0. Tap for more steps x2 + 11x 3 = 4 3. 3x^2+11x-4=0 por factorizacion Ver respuesta Publicidad Publicidad jackzotz jackzotz Respuesta: por formula cuadrática x=-4. It can factor expressions with polynomials involving any number of vaiables as well as more complex functions. Taking out the common terms. Algebra Factoring Calculator Step 1: Enter the expression you want to factor in the editor. Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work We shall now solve each term = 0 separately.200 x = 2 Step by step solution : Step 1 :Equation at the end of step 1 : (5x2 - 11x) + 2 = 0 Step 2 :Trying to factor by splitting the 5x2-13x-17=0 Two solutions were found : x = (13-√509)/10=-0. factorising the quadratic gives.333 x = 4 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 - 11x) - 4 = 0 Step 2 Loved by our community. Earlier we factored this polynomial by splitting the middle term.333333333 Steps Using Factoring By Grouping Steps Using the Quadratic Formula Steps for Completing the Square Steps Using Direct … Free quadratic equation calculator - Solve quadratic equations using factoring, complete the square and the quadratic formula step-by-step Algebra Solve Using the Quadratic Formula 3x^2-11x-4=0 3x2 − 11x − 4 = 0 3 x 2 - 11 x - 4 = 0 Use the quadratic formula to find the solutions. We can divide 0 by either binomial to cancel it out and focus on solving just one binomial. Procedimiento para factorizar la expresión. factorise root 3x 2 +11x+6root3. Substitute the values a = 4 a = 4, b = 0 b x2-11x+9=0 Two solutions were found : x = (11-√85)/2= 0. That's it. verified. igualas a 0 cada una X+4=0. Related Symbolab blog posts. 3x2 + 11x = 4. Hence 4 times 6x^2 = 24x^2. Q3.18 ÷ 0. Solve. →3x-1=0. Learn the basics, check your work, gain insight on different ways to solve problems. Solve : 3x-1 = 0 Add 1 to both sides of the equation : 3x = 1 Divide both sides of the equation by 3: x = 1/3 = 0. Polynomial Synthetic Division Calculator - apply polynomial synthetic division step-by-step. When x=0 then y=-4. Q1. Solving 3x 2 +11x-4 = 0 directly . Q1. To find the product, multiply 3x^2 by -4. Step 2. . Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. View Solution.1. The zeroes of the quadratic are x = − 1 3 and x = 4. −11±√112 −4⋅(3⋅10) 2 Solve the following quadratic equations by factorization: 3x 2 = −11x − 10.noitarepo detacidni eht mrofreP . 77 people found it helpful. Solve an equation, inequality or a system. 4- , ro 3/1=x→ . Factor by grouping. When x=-1, then y=10. Q3. Divide 2 x 3 + 3 x 2 − 11 x − 6 by x 2 + x − 6. x2+11x-210=0 Two solutions were found : x = 10 x = -21 Step by step solution : Step 1 :Trying to factor by splitting the middle term 1. let us now solve the equation by Completing The Square and by using the Quadratic Formula. 3X²+11X-4=0 por factorización paso a paso con comprobación por favor! Ver respuesta (3x-1)(x+4)=0 Publicidad Publicidad josesosaeric josesosaeric Tenemos que, realizando la factorización de la expresión dada por vamos a obtener como resultado .1 Factoring x2-11x-40 The first term is, x2 its coefficient is 3x2-11x-4=0 Two solutions were found : x = -1/3 = -0. Get all the terms with the wanted variable on one side of the equation and all the other terms on the other side. (3x+1) (x−4) = 0 Step 2: Set factors equal to 0. Example: 2x-1=y,2y+3=x. Divide each term in 3x2 + 11x = 4 by 3 and simplify. In mathematics, a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. 4. Step-1 : Multiply the coefficient of the first term by the constant 3 • -4 = -12. 3x2+11x+6 Final result : (3x + 2) • (x + 3) Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 + 11x) + 6 Step 2 :Trying to factor by splitting the middle term 3x2+11x+6=0 Two solutions were found : x = -3 x = -2/3 = -0. profile. 3x−1 = 0 3 x - 1 = 0 x+4 = 0 x + 4 = 0 Solve Solve for x x = −4 x = 31 ≈ 0. Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess GCD of x^4+2x^3-9x^2+46x-16 with x^4-8x^3+25x^2-46x+16; quotient of x^3-8x^2+17x-6 with x-3; remainder of x^3-2x^2+5x-7 divided by x-3; roots of x^2-3x+2; View more examples; Access instant learning tools. Substitute the values a = 4 a = 4, b = −11 b = - 11, and c = −3 c = - 3 into the quadratic formula and solve for x x. Calculator Examples » In the above equation 3x^2+11x-4 = 0, I understand where we need to find two numbers were a+b need to equal 11 to satisfy the 11x, however, I'm having trouble connecting where -12 came from where it states that we need to find numbers to satisfy (a)(b) = -12. This answer has been confirmed as correct and helpful. Get the x-intercepts. Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess GCD of x^4+2x^3-9x^2+46x-16 with x^4-8x^3+25x^2-46x+16; quotient of x^3-8x^2+17x-6 with x-3; remainder of x^3-2x^2+5x-7 divided by x-3; roots of x^2-3x+2; View more examples; Access instant learning tools. factorising expressions . Just like numbers have factors (2×3=6), expressions have factors ( (x+2) (x+3)=x^2+5x+6). Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 6. Next up in our Getting Started maths solutions series is help with another middle school algebra topic - solving Read More. 3x2 − 11x + 6 3 x 2 - 11 x + 6.0 = )3 - x ( )2 - x 3 ( 0 = )3− x()2−x3( spets erom rof paT . . -4/3 c. Quadratic equations such as this one can be solved by completing the square. For the zeros of 3x^2+11x-4, 3x^2+11x-4= 0. First, the expression needs to be rewritten as 3x^{2}+ax+bx-4. Supplement : Solving Quadratic Equation Directly Solving 3x 2-11x-4 = 0 directly . Just like numbers have factors (2×3=6), expressions have factors ( (x+2) (x+3)=x^2+5x+6). The value of (0. Step-by-step explanation: Let's solve your equation step-by-step. Parabola, Finding the Vertex : 4. If x = -3, then x^2 - 7x + 10 equals User: Solve 7x - 4 = 5x + 15 for x. x = -1/3. -x^2+3x+4. Use the quadratic formula to find the solutions. Factoring is the process Read More.resU ylniarB .1/3x^2-11x-4=0 solve for x, 3x^{2}-11x+6=0. Solving 3x 2 +11x-4 = 0 directly . Copied to clipboard. Enter a problem Cooking Calculators. The middle term is, +11x its coefficient is 11 . Now to solve for x. Any solution of term = 0 solves product = 0 as well.667 Step by step solution : Step 1 :Equation at the end of step 1 For 3x^2 - 11x - 4 to equal zero, one of its factors must be equal to zero. 3 ( 2x - 1 ) - 2( 3x + 4 ) = 11 x By Solving We get , 6x - 3 - 6x - 8 = 11x-11x = 11 One way is to get a zero (0) on one side of the inequality. View Solution.3 Solving 3x 2-11x+10 = 0 by the Quadratic Formula . Tap for more steps (3x−1)(x +4) = 0 ( 3 x - 1) ( x + 4) = 0 If … Solve Solve for x x = −4 x = 31 ≈ 0. Hence , required zeros are -1/3 and -4 . High School Math Solutions - Quadratic Equations Calculator, Part 3. 4/3 (More) The solution for the equation 2x^2 - x = 21 is {-3, 7/2}. Now , Verification. Solve : 3 x 2 + 11 x + 10 = 0. Q1. Algebra. Factor the expression by grouping. Rewrite as . Therefore, (0, -4) and (-1, 10) are the solutions of the given system of equation. Solution: The given quadratic equation is. 3x=0 and x+1=0. Algebra. For example: x2 −x −2 = 0. High School Math Solutions – Quadratic Equations Calculator, Part 3. The imaginary number i raised to the power of 38 simplifies to -1. heart. Substituting +8x +3x as 11x in the equation: Find k, if the equations 4 x 2 − 11 x + 2 k = 0 and x 2 − 3 x If the equations x 2 + 3 x + 2 = 0 and x 2 + k x + 6 = 0 have a common root then find the values of k. To solve this problem using division method, take any factor of the constant 6; let x = 2. (More) This answer has been confirmed as correct and helpful. Send us Feedback. For a polynomial of the form ax2 +bx+ c a x 2 + b x + c, rewrite the middle term as a sum of two terms whose product is a⋅c = 3⋅6 = 18 a ⋅ c = 3 ⋅ 6 = 18 and whose sum is b = −11 b = - 11. Step 4: Multiply carry-down by left term and put x2-11x-40 Final result : x2 - 11x - 40 Step by step solution : Step 1 :Trying to factor by splitting the middle term 1. Factor 3x^2-11x+6. So we get. Click here 👆 to get an answer to your question ️ Select the correct answer. Get step-by-step answers and hints for your math homework problems. 3x + 1=0 or x− 4=0 x = −1 /3 or x = 4. Earlier we factored this polynomial by splitting the middle term.1. 3x^{2}-11x=-4 . Divide the polynomial by x-2 to. Procedimiento para factorizar la expresión.1 Factoring 3x2+11x-4. Step 1: Write down the coefficients of 2x2 +3x+4 into the division table. Now , Verification. Share. Factoring is the process Read More.2) = 2 − 0.333333333 x = 4 Steps Using Factoring By Grouping Steps Using the Quadratic Formula Steps for Completing the Square Steps Using Direct Factoring … Online math solver with free step by step solutions to algebra, calculus, and other math problems.253 x = (-11+√421)/6= 1. The sum of roots of given quadratic equation Step-by-step explanation: Given quadratic equation We have to find the sum of roots. Now the clever bit: Take the coefficient of x , which is 11/3 , divide by two, giving 11/6 , and finally square it Find the Roots (Zeros) 3x^2+11x-4=0.333. 3 x 2 + 11 x - 4 = 0 ⇒ 3 x 2 - x + 12 x - 4 = 0 ⇒ x ( 3 x - 1) + 4 ( 3 x - 1) = 0 ⇒ ( 3 x - 1) ( x + 4) = 0 Answer: Option (a) is correct. 3x^{2}+11x-4=0. For chemistry, calculus, algebra, trigonometry, equation solving, basic math and more. Factorise: √3x 2 +11x+6√3. Solve by Factoring 3x^2-11x+6=0. Try this example now! » More Examples Trying the examples on the Examples page is the quickest way to learn how to use the … In the above equation 3x^2+11x-4 = 0, I understand where we need to find two numbers were a+b need to equal 11 to satisfy the 11x, however, I'm having trouble connecting where -12 came from where it states that we need to find numbers to satisfy (a)(b) = -12. Get all the terms with the wanted variable on one side of the equation and all the other terms on the other side.840 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 x = -5/3; x = -2; Correspondiente a la opción A En este caso tenemos la ecuación: 3x² + 11x + 10 = 0 Identificamos los elementos como: a = 3 / b = 11 / c = 10 Hallamos las dos raíces solución mediante al resolvente cuadrática: Primera raíz solución: Segunda raíz solución: Las soluciones para la ecuación son: The sum of the roots of 3x 2 + 11x - 4 = 0 is. Parabola, Finding the Vertex : 4. For a polynomial of the form ax2 +bx+ c a x 2 + b x + c, rewrite the middle term as a sum of two terms whose product is a⋅c = 3⋅−20 = −60 a ⋅ c = 3 ⋅ - 20 = - 60 and whose sum is b = −11 b = - 11.169 Step by step solution : Step 1 :Equation at the end of 2. +. Solving 3x 2-11x-4 = 0 directly . These values will be part of the solution since we have an 'or equal to' in the inequality. Jonathan and his sister Jennifer have a combined age of 48. Q4. 2 3 4.333 x = -1/2 = -0. 8,2 ÷ 2,05 ayiudaaaa porfa si alguienn entiendeeeeee Two numbers r and s sum up to \frac{11}{6} exactly when the average of the two numbers is \frac{1}{2}*\frac{11}{6} = \frac{11}{12}. Hence the positive x-intercept is (4, 0) Learn more on Middle School Math Solutions – Polynomials Calculator, Factoring Quadratics. 2 (6 - x) = x (x + 5), The sum of the roots of 3x^2 + 11x - 4 = 0 is and more. 3x + 5. The factors of √ 3 x 2 + 11 x + 6 Find the roots of the quadratic equation 3x^2 + 11x + 10 = 0 by method of - completing the Square. 3x(x-4) + 1(x-4) = 0 (3x+1) (x-4) = 0. Factorise: 3 x 2 + 11 x − 4 = 0. 3x2 + 11x - 4 = 0. Divide each term in 3x = 9 3 x = 9 by 3 3 and simplify. x + 1 x − 23 3x + 1 3x − 23 .890 x = (11+√85)/2=10. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a. 3x^{2}+11x-4=0. It is pretty strait forward if you Middle School Math Solutions – Polynomials Calculator, Factoring Quadratics. In order to complete the square, the equation must first be in the form x^{2}+bx=c. Copy. Divide 3x2 − 11x − 4 by x − 4. Parabola, Finding the Vertex : 4. Step 4.1 D -12. Step 3. If any individual factor on the left side of the equation is equal to 0 0, the entire expression will be equal to 0 0. The last term, "the constant", is -4. Divide both sides of the equation by 3 to have 1 as the coefficient of the first term : x2+ (11/3)x+ (4/3) = 0.15 (y − 0. Let's solve for x x x! Substituting the values of a a a, b b b, and c c c in Equation 1 1 1, we get: User: The sum of the roots of 3x 2 + 11x - 4 = 0 is a. Earlier we factored this polynomial by splitting the middle term. Then place the correct number in the box provided. f (x) = 3x4 − 11x3 − x2 + 19x + 6 f ( x) = 3 x 4 - 11 x 3 - x 2 + 19 x + 6. What is the remainder of 2x^2+7x -39/x-7.9/5. Similar Questions. Two numbers are in the ratio 11 ∶ 6 . 6. Copy. Limits. ⇒ 3x2 −11x −4 ≤ 0. let us now solve the equation by Completing The Square and by using the Quadratic Formula. dxd (x − 5)(3x2 − 2) Integration. Find the polynomial. We find out two factors whose sum is -11 and product is 12 3x = 10 + 1; 3x = 11; x = 11/3. Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is 11 . 3x^{2}+11x+4=0 .-1/3, 4 is the solution set of.5 (1 − y) find the midpoint of the points (1,2) and (3,-4) find the domain and range of (7,3),(-2,-2),(4,1),(4,1),(-9,0)(0,7) 7, 15, 23, 31, 39, 47, 55, 63; 0.. View Solution. heart. View Solution. Factor the expression by grouping. Steps Using Factoring By Grouping. I quite like the Euclidean algorithm. Talk to an Expert about this answer. 2)Product of zeros= -4/3= c /a x^2+2x+1=3x-10; 2x^2+4x-6=0; Show More; Description. 1/3 + (-4) = -11/3.5k points) quadratic equations; class-10; 0 votes. star. For the zeros of 3x^2+11x-4, 3x^2+11x-4= 0.2 Solving 3x2+11x+4 = 0 by Completing The Square . Solve Using the Quadratic Formula 3x^2-11x-4=0. The Factoring Calculator transforms complex expressions into a product of simpler factors.Popular Problems Algebra Solve by Factoring 3x^2+11x-4=0 3x2 + 11x − 4 = 0 3 x 2 + 11 x - 4 = 0 Factor by grouping. Sum = 1/3 - 4 = (1 - 12)/3 If 3x2 - 11x - 4 = (3x + 1)(x - 4), which equations should be solved to find the roots of 3x2 - 11x - 4 = 0? star. Simplify the following expression.

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Q2. Verified by Toppr. Given, zeroes of the polynomial 3x²+11x -4 are m and n ⇒ 3(m)² + 11(m) -4 = 0 ⇒ 3m²+ 11m -4 = 0 ⇒ 3m² +12m -m - 4 = 0 ⇒3m( m+ 4) - 1( m + 4) =0 ⇒ (3m - 1) ( m+4) = 0 ⇒ (3m - 1) = 0 (or) (m +4 ) = 0 ⇒ m = 1/3 or m = -4 if we replace n in x place , we get the same values Hence , m/n + n/m = 1 + 1 =2 hope it helps you. 1 Answer Nghi N Aug 4, 2017 -4; #1/3# Explanation: #3x^2 + 11x = 4# Divide both sides by 3: #x^2 + (11x)/3 = 4/3# #x^2 + (11x)/3 + 121/36 = 4/3 + 121/36# 6x2+11x+5 Final result : (6x + 5) • (x + 1) Step by step solution : Step 1 :Equation at the end of step 1 : ( (2•3x2) + 11x) + 5 Step 2 :Trying to factor by splitting the middle term 6x2+11x+4=0 Two solutions were found : x = -4/3 = -1. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -4 and q divides the leading coefficient 2. When we have this option, we have to do it both ways and see the different outcomes- we need both outcomes for a complete answer. Factor 3x^2-11x-20. asked Mar 22, 2022 in Quadratic Equations by Kshitijrathore (43. La ecuación factorizada: (x+4)(3x-1) Explicación paso a paso: Publicidad Publicidad Nuevas preguntas de Matemáticas. The product of the diamond problem is -12x^2. Algebra Factor 3x^2-11x-4 3x2 − 11x − 4 3 x 2 - 11 x - 4 For a polynomial of the form ax2 +bx+ c a x 2 + b x + c, rewrite the middle term as a sum of two terms whose product is a⋅c = 3⋅−4 = −12 a ⋅ c = 3 ⋅ - 4 = - 12 and whose sum is b = −11 b = - 11.1 Factoring x2+11x-210 The first term is, x2 Verified answer. Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0. Q5. [1] There are three main ways to solve quadratic equations: 1) to factor the quadratic equation if you can do so, 2) to use the quadratic formula, or 3) to complete the square. 3x+1 = 0. 3x^{2}-11x+4-4=-4 . .(1) y = 3x² − 11x − 4. Detailed step by step solution for 5x^2-11x+4=0. 3x^2-11x+4=0 2. Save to Notebook! Sign in. 3x^2 + 11x - 4 = 0; (3x - 1) (x + 4) = 0; 3x - 1 = 0; 3x = 1; x = 1/3; x + 4 = 0; x = -4; The sum of the roots of 3x^2 + 11x - 4 = 0 is -11/3. .1 Find the Vertex of y = 3x 2-11x-4 Parabolas have a highest or a lowest point called the Vertex . Q2. Related Symbolab blog posts. Difference of Squares: a2 – b2 = (a + b)(a – b) a 2 Factorise 3x^2 + 11x 4 = 0 Get the answer to this question and access other important questions, only at BYJU’S. Step-4 : Add up the first 2 terms, pulling out like factors : x • (2x+1) Add up the last 2 terms, pulling out common factors : 3 • (2x+1) Two numbers r and s sum up to 11 exactly when the average of the two numbers is \frac{1}{2}*11 = \frac{11}{2}. Explore math with our beautiful, free online graphing calculator. x ^ 2 +\frac{11}{3}x -\frac{4}{3} = 0. The sun of the roots of 3x^2+11x-4=0. x=0 and x=-1.586 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 + 11x) - 25 = 0 Step 2 :Trying 5x2+11x-2=0 Two solutions were found : x = (-11-√161)/10=-2. x2+11x-210=0 Two solutions were found : x = 10 x = -21 Step by step solution : Step 1 :Trying to factor by splitting the middle term 1. If their HCF is 4, find the smallest number. 3x 2 - 11x + 6 = 0. Select the correct answer from the drop-down menu. en. Solving 3x 2-11x-4 = 0 directly . 4x2 − 11x − 3 = 0 4 x 2 - 11 x - 3 = 0. 3x^2-11x-4=0. Explore similar answers. Answer: option B. Not sure where -12 came from. Move all terms to the left side of the equation and simplify.556 Step by step solution : Step 1 :Equation at the end of step 1 A quadratic equation is a polynomial equation in a single variable where the highest exponent of the variable is 2. Step 1. Send us Feedback. Q5. Save to Notebook! Sign in. Brainly User. Solve quadratic equations step-by-step. Q2. For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is . Divide 3x2 − 11x − 4 by x − 4. Divide both sides of the equation by 3: x = -1/3 = -0. . Next up in our Getting Started maths solutions series is help with another middle school algebra topic - solving Read More. Step-1 : Multiply the coefficient of the first term by the constant 3 • 30 = 90. View Solution. report flag outlined. verified. Now that we know what the sum and product of the diamond problem is, we need to find two terms that multiply to Algebra. 3x+1 = 0. Parabola, Finding the Vertex : 4. →(3x-1)(x+4)=0. Pull terms out from under the radical, assuming positive real numbers. Earlier we factored this polynomial by splitting the middle term. 4. 50. .8/5. Send us Feedback. 2. 1. x=1/3. The answer is (3x - 1) and (x + 4). Now solve the quadratic equation (x 2 - 4x + 3) = 0 to get x= 1 or x = 3. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 … Algebra Factor 3x^2-11x-4 3x2 − 11x − 4 3 x 2 - 11 x - 4 For a polynomial of the form ax2 +bx+ c a x 2 + b x + c, rewrite the middle term as a sum of two terms whose product is … Steps Using Direct Factoring Method View solution steps Graph Graph Both Sides in 2D Graph in 2D Quiz Quadratic Equation 3x2 −11x+4 = 0 Similar Problems from Web … Solve for x x = − 31 ≈ −0. Solve the cubic equation x 3 - 6 x 2 + 11x - 6 = 0. Verified answer. To learn more on Equation User: (12x 2 - 10x -12) ÷ (3x + 2) Weegy: When you multiply and simplify (x + 4) (x^2 - 3x + 2) you get the result of x^3 + x^2 - 10x + 8. Middle School Math Solutions - Inequalities Calculator. Factorise: √3x 2 +11x+6√3. 3x2 + 2 = 11 − x2 3 x 2 + 2 = 11 - x 2. 3x^2 + 11x - 4 = 0 x^2 + (11/3)x = 4/3 (x+11/6)^2 = 169/36 Step-by-step explanation: heart outlined. Starting at $5. A discount of 10% given on marked price. The function will become 3x²-11x-4 = 0. Factor out the 4. 3x - 1 = 0 and x + 4 = 0. Step 4. 1)sum of zeros = 1/3-4= -11/4 = -b/a . Copy. heart outlined. a+b=-11 ab=3\left(-4\right)=-12 . 3x2 + 11x - 4 = 0. 3x^2 + 11x -4=0 ax^2 +bx +c=0 Multiply ac to get -12 find factors the multiply to get -12 and add to get the coefficient of the middle term +11 Because we want -12, one factor is negative and the other is positive. Find the Roots (Zeros) f (x)=3x^4-11x^3-x^2+19x+6. Example 5. factorise root 3x 2 +11x+6root3. Solve your math problems using our free math solver with step-by-step solutions. 3x2 + 11x + 10 = 0 3 x 2 + 11 x + 10 = 0. Get help on the web or with our math app. 7/4. quadratic-equation-calculator. What is the remainder of 2x^2+7x -39/x-7. 5 /5. Study with Quizlet and memorize flashcards containing terms like Using the quadratic equation to solve 3x^2 + 11x - 4 = 0, the value of b^2 - 4ac is, Solve the following problem for the roots by using the quadratic formula. en. Given that m and n are the zeroes of the polynomial 3 x 2 + 11 x − 4. To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b. (3x +1)(x −4) ≤ 0.1 Find the Vertex of y = 3x 2 +11x-4 Parabolas have a highest or a lowest point called the Vertex . Answer: B.7 C. Add 4 to both sides of the equation. ALJABAR Kelas 9 SMP. 11 ±√(−11)2 −4⋅(4⋅− The right choice is B. Free Factor Trinomials Calculator - Factor trinomials step-by-step. The Extended part can be done as a continued fraction, same steps as for integers.0/5. Get help on the web or with our math app. View Solution. Solve for x. Free Factor Trinomials Calculator - Factor trinomials step-by-step. Hence the negative x-intercept is (-1/3, 0) Also, x-4 = 0. let us now solve the equation by Completing The Square and by using the … 3x2 + 11x − 4. This answer has been confirmed as correct and helpful. Enter a problem Cooking Calculators. We now require to consider the 'less than' part of the 3x2-11x-20=0 Two solutions were found : x = -4/3 = -1. 3x −1 = 0 → 3x = 1 → x = 1 3.333 x = 5 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 - 11x) - 20 = 0 Step 2 :Trying to factor by splitting 3x2-11x-42 Final result : (x - 6) • (3x + 7) Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 - 11x) - 42 Step 2 :Trying to factor by Differentiation. add and simplify (2x^2-11x)+ (3x^2+10x-4) the answers are either - 6x^2-11x-4 5x^4 5x^2-x-4 5x^2-4. I'm seeing a -4 at the end of the equation. We need to solve both. Subtract 4 from both sides of the equation. (x-4) is a factor of 3x^2 - 11x -4.1 Find the For example, enter 3x+2=14 into the text box to get a step-by-step explanation of how to solve 3x+2=14. Because we want the sum to be +11, the factor with greater absolute value is the positive factor: List: -1xx12 sum -1+12 = 11 STOP Factoring Calculator. Solve by Completing the Square 3x^2+11x-4=0.. factorising expressions .ppA ni nepO . It is pretty strait forward if you Middle School Math Solutions - Polynomials Calculator, Factoring Quadratics. 1. Step 1. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics 3x2 - 11x + 6 = 0. x→−3lim x2 + 2x − 3x2 − 9. Click here 👆 to get an answer to your question ️ Using the quadratic equation to solve 3x^2+11x-4=0, the value of b^2-4ac is -26 73 169.srewsna wen on era erehT . (x 2 - 4x + 3) = 0. . The function will become 3x²-11x-4 = 0. (3x + 1) and (x - 4) (3x - 1) and (x + 4) (3x - 2) and (x + 2) (3x + 2) and (x - 2) I assume that the correct equation is 3x2 + 11x - 4. Solve Using the Quadratic Formula 3x^2+11x+10=0. User: Solve |4x - 8| User: Solve the following inequality.1 Find the Vertex of y = 3x 2 +11x-4 Parabolas have a highest or a lowest point called the Vertex . Steps Using the Quadratic Formula. 3x 2 – 11x + 6 = 0. let us now solve the equation by Completing The Square and by using the Quadratic Formula. 3x2 + 11x = 4. So Solve the two equations for zero: 3x+1=0 x-4=0. Get help on the web or with our math app. verified. 2 2 2 3 4. en. 3x²+3x=0. View Solution. Use the quadratic formula to find the solutions. ALJABAR. h (x) = x² + 3x g (x) = -x +4 Find h (g (-x) A. Solve Using the Quadratic Formula 4x^2-11x-3=0.667 x = 3 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 - 11x) + 6 = 0 Step 2 the discriminant is: Δ = b2 − 4ac. Simplify. let us now solve the equation by Completing The Square and by using the Quadratic Formula. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a. View Solution. W0lf93. Q5.1 Factoring x2-11x+9 3x2-11x+6=0 Two solutions were found : x = 2/3 = 0. Solve Using the Quadratic Formula 3x^2+2=11-x^2. Tap for more steps x = 3 x = 3. Substitute the values , , and into the quadratic formula and solve for .1 Find the Vertex of y = 3x 2 +11x-4 Parabolas have a highest or a lowest point called the Vertex . Advertisement. Related Symbolab blog posts. Substitute the values a = 3 a = 3, b = 11 b = 11, and c = 10 c = 10 into the quadratic formula and solve for x x. Was this answer helpful? 2. Therefore: -x^2 + 9 - 3x^2 - 11x + 4 goes to -4x^2 + 13 - 11x. Polynomial Synthetic Division Calculator - apply polynomial synthetic division step-by-step. Was this answer helpful? 2. ∫ 01 xe−x2dx. x ^ 2 +\frac{11}{3}x +\frac{4}{3} = 0. Quadratic equations such as this one can be solved by a new direct factoring method that Algebra. Answer rating 5. If the zeroes of the polynomial x 3 − 3 x 2 + x + 1 are m - n, m and m + n, find m and n. Divide both sides of the equation by 3: x = -1/3 = -0. If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the Step-by-step explanation: 6x^2+11x +4. 3x^2 - 11x - 4 = 0. Consider the given quadratic equation For a given standard quadratic equation , we have Sum of roots is given by and product of roots is given by Thus, for the given quadratic equation 2 2. x = 1/3 and x = -4. 3 { x }^{ 2 } +11x-4. How do you factor and solve 3x2 + 11x − 4 = 0? Algebra Quadratic Equations and Functions Comparing Methods for Solving Quadratics 1 Answer lechugamaestro19 Mar 5, 2018 x = 1 3 or − 4 Explanation: In this quadratic, the coefficient of the squared term gives us a big hint on how to factor this.500 Step by step solution : Step 1 :Equation at the end of step 1 : ( (2•3x2 3 x − 5 = 25 − 3 x; 2 x 2 + 55 x − 87 = 0; graph of a circle with radius 10 and center at (15,-3) 2, 9, 16, 23, 30; 0. We see that 3 x 2 − 11 x − 4 = 0 3x^2-11x-4=0 3 x 2 − 11 x − 4 = 0 has the form a x 2 + b x + c = 0 ax^2+bx+c=0 a x 2 + b x + c = 0, where a = 3 a=3 a = 3, b = − 11 b=-11 b = − 11, and c = − 4 c=-4 c = − 4. Free calculus calculator - calculate limits, integrals, derivatives and series step-by-step. Solve 3x^2+11x+10=0 | Microsoft Math Solver. x-4=0 can be solved by adding 4 on both sides resulting in x=4. Hence the negative x-intercept is (-1/3, 0) Also, x-4 = 0. Factor the expression by grouping.0 (%counter% votes) Log in to add comment. verified. 3x²−11x−4=0 Step 1: Factor left side of equation. First, the expression needs to be rewritten as 3x^{2}+ax+bx-4. 2(6 - x) = x(x + 5), The imaginary number i raised to the power of 38 simplifies to and more. Solve by Completing the Square 3x^2+11x-4=0. Find the roots of 3 x 2 − 11 x + 6 = 0. en. x = -1/3. To solve the equation for different variables step-by-step clear any fractions by multiplying both sides of the equation by the LCM of the denominators. Similar Problems from Web Search.00/month. (3x^2 - 11x - 4) - (x - 2) (2x + 3) Answer … 5x2-11x+2=0 Two solutions were found : x = 1/5 = 0. Factorise: 3 x 2 + 11 x − 4 = 0. Verified answer. Use the quadratic formula to find the solutions. x = 4. star. x (3x - 1) + 4 (3x - 1) = 0 (3x - 1) (x + 4) = 0. Share. 1 answer.001 is: Q4. 9. Matematika. the sum of the root of 3x^2+11x-4=0. Search for an answer or ask Weegy. Solution. The discriminant can be used to characterize the solutions of the equation as: 1) Δ > 0 two separate real solutions; 2) Δ = 0 two coincident real solutions (or one repeated root); 3) Δ < 0 no real solutions. 1) BFS. Earlier we factored this polynomial by splitting the middle term. 3X-1=0. 3x−2 = 0 3 x - 2 = 0. If a, b and c are the roots of the polynomial 3x³ + 11x - 22 and sum of the roots is 0, then find the value of a³ + b³ + c³. 3x 2 + 11x - 4 = 0 .1. The final solution is all the values that make 3 { x }^{ 2 } -11x-4.