To find the zeros of the function [tex]\(f(x) = x^2 - 10x + 25\)[/tex], we need to determine the values of [tex]\(x\)[/tex] for which the function equals zero.
1. Start by setting the function equal to zero:
[tex]\[
x^2 - 10x + 25 = 0
\][/tex]
2. We observe that the quadratic equation can be factored. Notice that the quadratic term and the constant term can be expressed as a perfect square:
[tex]\[
x^2 - 10x + 25 = (x - 5)^2
\][/tex]
3. Now, we set the factored form equal to zero:
[tex]\[
(x - 5)^2 = 0
\][/tex]
4. Solving for [tex]\(x\)[/tex], take the square root of both sides:
[tex]\[
x - 5 = 0
\][/tex]
5. Add 5 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x = 5
\][/tex]
Therefore, the only zero of the function [tex]\(f(x) = x^2 - 10x + 25\)[/tex] is [tex]\(x = 5\)[/tex].
The correct answer to the question is:
A. [tex]\(x = 5\)[/tex] only
