The value(s) of satisfying the equation is/are

MATHEMATICS · Single correct · AoPS · Mathematics · Special Factorizations · Special Factorizations

Problem

The value(s) of

x

satisfying the equation

x^9 + \frac{9}{8}x^6 + \frac{27}{64}x^3 - x + \frac{219}{512} = 0

is/are (A)

\frac{-1 + \sqrt{13}}{4}

(B)

-\frac{1}{2}

(C)

\frac{-1 - \sqrt{13}}{4}

(D)

\frac{1}{2}