kundrus1234
contestada

g(x)=x
2
+5x−14g, left parenthesis, x, right parenthesis, equals, x, start superscript, 2, end superscript, plus, 5, x, minus, 14
1) What are the zeros of the function?
Write the smaller xxx first, and the larger xxx second.
\text{smaller }x=

Respuesta :

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ANSWER

[tex]x = - 7\: or \: x = 2[/tex]

EXPLANATION

The given function is

[tex]g(x) = {x}^{2} + 5x - 14[/tex]

To find the zeros of this function, we set the equation to zero.

[tex]{x}^{2} + 5x - 14 = 0[/tex]

Split the middle term

[tex] {x}^{2} + 7x - 2x - 14 = 0[/tex]

Factor:

[tex]x(x + 7) - 2(x + 7) = 0[/tex]

Factor further,

[tex](x + 7)(x - 2) = 0[/tex]

By the zero product property,

[tex]x + 7 = 0 \: or \: x - 2 = 0[/tex]

Solve for x.

[tex]x = - 7\: or \: x = 2[/tex]

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