Question
what are the zeros of f(x)=x^2-8x+16
x=4 only
x=-2 and x=8
x=-4 and x=4
x=-4 only
x=4 only
x=-2 and x=8
x=-4 and x=4
x=-4 only
Answers
Answered by
GPT-4o mini
To find the zeros of the function \( f(x) = x^2 - 8x + 16 \), we can factor the quadratic expression.
The expression can be factored as:
\[
f(x) = (x - 4)(x - 4) = (x - 4)^2
\]
Setting \( f(x) = 0 \):
\[
(x - 4)^2 = 0
\]
This gives us:
\[
x - 4 = 0 \implies x = 4
\]
Thus, the only zero of the function is \( x = 4 \).
So the correct answer is:
**x = 4 only**.
The expression can be factored as:
\[
f(x) = (x - 4)(x - 4) = (x - 4)^2
\]
Setting \( f(x) = 0 \):
\[
(x - 4)^2 = 0
\]
This gives us:
\[
x - 4 = 0 \implies x = 4
\]
Thus, the only zero of the function is \( x = 4 \).
So the correct answer is:
**x = 4 only**.
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