Answer:
[tex]x=6[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=x^2-12x+36[/tex]. We are asked to find the zeros of our given function.
We can recognize from our given function formula that it is a perfect square as:
[tex]f(x)=x^2-12x+36=x^2-(2*6*x)+6^2=(x-6)^2[/tex]
Using zero product property we will get:
[tex](x-6)^2=0[/tex]
Upon taking square root of both sides, we will get:
[tex]x-6=0[/tex]
Upon adding 6 on both sides, we will get:
[tex]x-6+6=0+6[/tex]
[tex]x=6[/tex]
Therefore, [tex]x=6[/tex] is a zero for our given function.
