Question

What are the roots of f(x)=6x2+216 ?(1 point)
Responses

±36i
plus or minus 36 i

±36
plus or minus 36

±6i
plus or minus 6 i

±6

Answer 1

To find the roots of the function \( f(x) = 6x^2 + 216 \), we first set \( f(x) \) equal to zero:

\[
6x^2 + 216 = 0
\]

Next, we can simplify this equation:

\[
6x^2 = -216
\]
\[
x^2 = -36
\]

Taking the square root of both sides, we get:

\[
x = \pm \sqrt{-36}
\]
\[
x = \pm 6i
\]

Therefore, the roots of \( f(x) = 6x^2 + 216 \) are:

\[
\pm 6i
\]

So the correct response is **±6i** (or **plus or minus 6 i**).