Question
What are the zeros of f(x)=−4(2x+3)3(6−x) (1 point) Responses −32, 6 −32, 6 −32, 6, −4 −32, 6, −4 −32, 6, 0 −32, 6, 0 32, −6
Answers
Answered by
GPT-4o mini
To find the zeros of the function \( f(x) = -4(2x + 3)^3(6 - x) \), we need to set \( f(x) = 0 \) and solve for \( x \).
Since the function is a product of terms, it will equal zero if any of the individual factors equal zero.
1. **Set the factor \( (2x + 3)^3 = 0 \)**:
\[
2x + 3 = 0 \\
2x = -3 \\
x = -\frac{3}{2}
\]
2. **Set the factor \( (6 - x) = 0 \)**:
\[
6 - x = 0 \\
x = 6
\]
Thus, the zeros of the function are \( x = -\frac{3}{2} \) and \( x = 6 \).
Now looking at the responses provided, it appears none of the given options include \( -\frac{3}{2} \). The closest option might suggest that there is a misunderstanding. The zeros derived from the calculation determine that the actual zeros of the function are:
**Final Zeros**: \( -\frac{3}{2}, 6 \)
If we compare options again, none of the answers seems directly derivable from the calculating steps. Please check the answer choices provided here, as the discrepancy could be noted therein.
Since the function is a product of terms, it will equal zero if any of the individual factors equal zero.
1. **Set the factor \( (2x + 3)^3 = 0 \)**:
\[
2x + 3 = 0 \\
2x = -3 \\
x = -\frac{3}{2}
\]
2. **Set the factor \( (6 - x) = 0 \)**:
\[
6 - x = 0 \\
x = 6
\]
Thus, the zeros of the function are \( x = -\frac{3}{2} \) and \( x = 6 \).
Now looking at the responses provided, it appears none of the given options include \( -\frac{3}{2} \). The closest option might suggest that there is a misunderstanding. The zeros derived from the calculation determine that the actual zeros of the function are:
**Final Zeros**: \( -\frac{3}{2}, 6 \)
If we compare options again, none of the answers seems directly derivable from the calculating steps. Please check the answer choices provided here, as the discrepancy could be noted therein.