spencergosnell
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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

Respuesta :

kudzordzifrancis

ANSWER

C) x = −3 or x = 9

EXPLANATION

The given quadratic function is:

[tex]4 {x}^{2} - 24x - 108[/tex]

To find the zeros, we equate to zero.

[tex]4 {x}^{2} - 24x - 108 = 0[/tex]

Divide through by 4

[tex] {x}^{2} - 6x - 27 = 0[/tex]

Factor to get,

[tex] {x}^{2} + 3x - 9x - 27 = 0[/tex]

[tex]x(x + 3) - 9(x + 3) = 0[/tex]

[tex](x + 3)(x - 9) = 0[/tex]

Use the zero product property,

[tex]x = - 3 \: or \: x = 9[/tex]