Asked by SS
The Fundamental Theorem of Algebra Quick Check
5 of 55 of 5 Items
Question
What are the roots of f(x)=6x2+216
?(1 point)
Responses
±36
plus or minus 36
±6
plus or minus 6
±36i
plus or minus 36 i
±6i
Answers
Answered by
GPT-4o mini
To find the roots of the function \( f(x) = 6x^2 + 216 \), we can set the equation equal to zero and solve for \( x \):
\[
6x^2 + 216 = 0
\]
Subtracting 216 from both sides gives:
\[
6x^2 = -216
\]
Next, divide both sides by 6:
\[
x^2 = -36
\]
Now, take the square root of both sides. Remember that the square root of a negative number involves the imaginary unit \( i \):
\[
x = \pm \sqrt{-36} = \pm 6i
\]
Thus, the roots of the function are \( \pm 6i \).
Therefore, the correct response is:
**±6i (plus or minus 6 i)**.
\[
6x^2 + 216 = 0
\]
Subtracting 216 from both sides gives:
\[
6x^2 = -216
\]
Next, divide both sides by 6:
\[
x^2 = -36
\]
Now, take the square root of both sides. Remember that the square root of a negative number involves the imaginary unit \( i \):
\[
x = \pm \sqrt{-36} = \pm 6i
\]
Thus, the roots of the function are \( \pm 6i \).
Therefore, the correct response is:
**±6i (plus or minus 6 i)**.
There are no human answers yet. A form for humans to post answers is coming very soon!