Follow the following steps to find all three roots of the equation x³ + 3x² - 6x + 20 = 0. (a) Use appropriate substitution to get rid of the quadratic term 3x² in the above equation. (b) Apply Cardano's formula to find a real root ₁ of the original equa- tion. (c) Use long division to get a quadratic equation for the two remaining (imaginary) roots a2 and a3. (d) Using the quadratic formula, find a2 and a3. (e) By a direct computation verify Vieta's formulas -3, -6, a1a2a3 = -20. a₁ + a₂ + az = a1a2 + a1a3 + α2α3 =

Q: If x = 2 is one of the roots of P(x) = bx? – 12x + 4, find b.

A:

Q: 1. Consider the equation (2¹ +64) = 32√√3³. Find all the roots and express them in rectangular form.…

A:

Q: Use the quadratic formula to find the roots following quadratic: y = x² + 4x +5

A:

Q: Find the roots of the equation -45a? – 35x + 100 = 0 using Bisection Method. Positive root: [ Choose…

A:

Q: (b) The roots of the quadratic equation 3x-11x+9=0 are a and B. Form a quadratic equation whose…

A:

Q: A. Find the sum and product of the solutions of the following quadratic equations. Quadratic…

A: sum of root =-b/a product of root =c/a

Q: (b) The quadratic equation x² + px + q = 0 in which the coefficients p and q are real, has a complex…

A: Sol

Q: Find one of the four solutions of (6x – 9x +4) -5(6z - 9x + 4) +5 = 0. Write your solution using…

A: To solve: 6x2-9x+42-56x2-9x+4+5=0 Substitute 6x2-9x+4 = y

Q: Given a cubic equation,            Find the roots of the equation by completing the following…

A: Find the roots of cubic equation using synthetic division

Q: 1. Solve the following equations and list all the roots. a) (x² – 25)(x² + 5x – 14) = 0 b) (2x +…

A: Simplify the equation then find roots.

Q: Find ‘m’ for which the equation (? − 12)? 2 + 2(? − 12)? + 2 = 0 has equal roots.

A:

Q: When Abraham jumps into the air, his height in feet above the surface of the water is given by h =…

A: We have given a function that models the height in feet above the surface of the water, h(t)=-16…

Q: Determine the roots of the following quadratic expression 4x² - 19x + 12 = 0 a) x=3 and x=-16 b) x =…

A:

Q: 29. Use the quadratic formula to find the roots of the following quadratic: y = 2x² – 11x + 5 -

A:

Q: Find the roots: x3 = 2 - 3i

A:

Q: Answer the following: 1. Characterize the roots of the following quadratic equations using the…

A:

Q: If a and B are the roots of the quadratic equation -x+6x - 4 = 0, find the values of the following…

A:

Q: Use DeMoivre’s theorem to find the cube roots of 8 (i.e. let’s solve the equation z3 = 8 for z).

A:

Q: Find @Er Er? © Ene for -2x3 +5X-4=0 if riz Yo grz ane the roots.

A:

Q: 2. Find the roots of the following functions using the method indicated. a. -2x² + 8x - 30 Complete…

A: Given, Find roots for the following using indicated method

Q: 1. Solve for x: 2x - 4x +7= 0. Write any complex solutions in terms of i and simplify any square…

A: The given equation is 2x2-4x+7=0. Calculate the complex solutions in terms of i and simplify any…