Question

What are the solutions to the equation 0 = x2 – x – 6? Check all that apply.

x = –3
x = –2
x = 0
x = 2
x = 3

Answer 1

Option 2 and 5.

The solution of the equation is x=-2 and x=3.

Explanation:

Given : Equation
`x^2-x-6=0`

To find : What are the solutions to the equation? Check all that apply.

Solution :

Equation
`x^2-x-6=0`

Substitute all values from options which satisfy the equation is the solution.

1) x=-3

`(-3)^2-(-3)-6=0`

`9+3-6=0`

`12-6=0`

`6\\eq 0`

2) x=-2

`(-2)^2-(-2)-6=0`

`4+2-6=0`

`6-6=0`

`0= 0`

3) x=0

`(0)^2-(0)-6=0`

`0-0-6=0`

`-6\\eq 0`

4) x=2

`(2)^2-(2)-6=0`

`4-2-6=0`

`-4\\eq 0`

5) x=3

`(3)^2-(3)-6=0`

`9-3-6=0`

`0=0`

The solution of the equation is x=-2 and x=3.

Answer 2

To factor this equation out, the easiest way is to solve for the two x values that add up to -1 but when multiplied is equal to -6. It should look like this: (x +- ?)(x +- ?).
The factored out form is then (x - 3)(x +2), because -3 + 2 = -1 and when multiplied together gives -6.
x - 3 = 0
x = 3
x + 2 = 0
x = -2
The two solutions are therefore, x = 3 and x = -2.