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).
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