Question

What are the roots of the polynomial equation x^3-7xx=6x-12? use a graphing calculator and a system of equations.

A. -6, 6

B. -4, 1, 3

C. -3, -1, 4

D. 1, 3​

Answer 1

Answer: ITS B (-4,1,3)

Answer 2

The roots of the polynomial equation x^3 - 7x = 6x - 12 is 1, 3, -4 Hence option B is correct

Solution:

Given that the polynomial equation is
`x^(3)-7 x=6 x-12`

We are asked to find the roots of the polynomial

`x^(3)-7 x=6 x-12`

`x^(3)-7 x-6 x+12=0`

On solving we get,

`x^(3)-13 x+12=0`

`x^(3)-12 x-x+12=0`

`\begin{array}{l}{x\left(x^(2)-1\right)-12(x-1)=0} \\\\ {x\left(x^(2)-1\right)-12(x-1)=0}\end{array}`

(x-1)(x(x+1)-12)=0

(x-1)(x-3)(x+4)=0

x = 1, 3, -4

Hence the roots of the polynomial equation x^3 - 7x = 6x - 12 is 1, 3, -4 Hence option B is correct