To find the roots of the function \( f(x) = 6x^2 + 216 \), we can set it equal to zero:
\[ 6x^2 + 216 = 0 \]
Now, we can isolate \( x^2 \):
\[ 6x^2 = -216 \]
\[ x^2 = -36 \]
Next, we take the square root of both sides:
\[ x = \pm \sqrt{-36} \]
Since \(\sqrt{-36} = \sqrt{36} \cdot i = 6i\), we have:
\[ x = \pm 6i \]
Thus, the roots of the function \( f(x) = 6x^2 + 216 \) are:
±6i
So the correct response is: ±6i (plus or minus 6 i).