If the real roots of the equation 3 x to the 4th power minus 6 x cubed plus 3 x squared minus 54 x minus 216 is equal to 0 are negative 2 and 4 , what are the nonreal roots?

The two known real roots give the factor (x + 2)(x − 4) = x² − 2x − 8. Dividing the polynomial by 3(x² − 2x − 8) leaves x² + 9, so the remaining roots satisfy x² = −9. Therefore the nonreal roots are −3i and 3i, choice D.

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