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].
