Question

What are the roots of the polynomial equation x^3-7x=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

The correct answer is B. -4, 1, 3
Hope this helps!!

Answer 2

The roots are x = -4, 1 and 3.

B is the correct option.

Explanation:

We have to find the roots of the polynomial
`x^3-7x=6x-12`

We can find the roots by forming a system of equations and with the help of a graphing calculator.

The system of equations for the given polynomial:

`y=x^3-7x........(1)\\y=6x-12..........(2)`

Now, we graph these equations in the xy-plane. The x-coordinate (s) of the intersection point will be the roots of the equation.

The graph is shown in the attached file.

The intersection points are (-4,-36),(1,-6) and (3,6). The x-coordinates are x = -4,1 and 3.

Therefore, the roots are x = -4, 1 and 3.

B is the correct option.