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What are the zeros of this function?

[tex]\[ g(x) = 2(x + 2)(x - 9) \][/tex]

The zeros of function [tex]\( g \)[/tex] are located at [tex]\(\square\)[/tex] and [tex]\(\square\)[/tex].

Sagot :

GinnyAnswer
To find the zeros of the function [tex]\( g(x) = 2(x+2)(x-9) \)[/tex], we need to determine the values of [tex]\( x \)[/tex] that make [tex]\( g(x) = 0 \)[/tex].

Start by setting the function equal to zero:
[tex]\[ 2(x + 2)(x - 9) = 0 \][/tex]

The product of these factors is zero if and only if at least one of the factors is zero. This can be written as:
[tex]\[ (x + 2)(x - 9) = 0 \][/tex]

Now we solve for [tex]\( x \)[/tex] by setting each factor equal to zero separately:

1. For the first factor:
[tex]\[ x + 2 = 0 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = -2 \][/tex]

2. For the second factor:
[tex]\[ x - 9 = 0 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 9 \][/tex]

Thus, the zeros of the function [tex]\( g \)[/tex] are located at [tex]\( -2 \)[/tex] and [tex]\( 9 \)[/tex].

So, the correct answers to fill in the blanks are:

The zeros of function [tex]\( g \)[/tex] are located at [tex]\( \boxed{-2} \)[/tex] and [tex]\( \boxed{9} \)[/tex].
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