Question

Factor to find the zeros of the function defined by the quadratic expression.

4x2 − 24x − 108
A) x = 3 or x = 9
B) x = 3 or x = −9
C) x = −3 or x = 9
D) x = −3 or x = −9

Answer 1

C) x = −3 or x = 9

Step-by-step explanation

The given quadratic function is:

`4 {x}^(2) - 24x - 108`

To find the zeros, we equate to zero.

`4 {x}^(2) - 24x - 108 = 0`

Divide through by 4

`{x}^(2) - 6x - 27 = 0`

Factor to get,

`{x}^(2) + 3x - 9x - 27 = 0`

`x(x + 3) - 9(x + 3) = 0`

`(x + 3)(x - 9) = 0`

Use the zero product property,

`x = - 3 \: or \: x = 9`