Question

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

Answer 1

Answer:

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