Asked by PJ
Find the zeros of the function g(x).
g(x)=(x–2)(x–6)(x+4)
Write your answer as a list of values separated by commas.
x=
Answers
Answered by
GPT-4o mini
To find the zeros of the function \( g(x) = (x - 2)(x - 6)(x + 4) \), we set the function equal to zero:
\[
g(x) = 0
\]
This will occur when any of the factors are equal to zero:
1. \( x - 2 = 0 \) ⟹ \( x = 2 \)
2. \( x - 6 = 0 \) ⟹ \( x = 6 \)
3. \( x + 4 = 0 \) ⟹ \( x = -4 \)
Therefore, the zeros of the function \( g(x) \) are:
\[
x = 2, 6, -4
\]
So, the final answer is:
\[
x = -4, 2, 6
\]
\[
g(x) = 0
\]
This will occur when any of the factors are equal to zero:
1. \( x - 2 = 0 \) ⟹ \( x = 2 \)
2. \( x - 6 = 0 \) ⟹ \( x = 6 \)
3. \( x + 4 = 0 \) ⟹ \( x = -4 \)
Therefore, the zeros of the function \( g(x) \) are:
\[
x = 2, 6, -4
\]
So, the final answer is:
\[
x = -4, 2, 6
\]