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What are the zeros of [tex]\( f(x) = x^2 - 10x + 25 \)[/tex]?

A. [tex]\( x = 5 \)[/tex] only
B. [tex]\( x = -5 \)[/tex] and [tex]\( x = 5 \)[/tex]
C. [tex]\( x = -5 \)[/tex] only
D. [tex]\( x = -5 \)[/tex] and [tex]\( x = 10 \)[/tex]

Sagot :

GinnyAnswer
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
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