2004 AMC 12B Problem 17

For some real numbers a and b, the equation 8x^3 + 4ax^2 + 2bx + a = 0 has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 5, what is the value of a?

\mathrm{(A)}\ -256 \qquad\mathrm{(B)}\ -64 \qquad\mathrm{(C)}\ -8 \qquad\mathrm{(D)}\ 64 \qquad\mathrm{(E)}\ 256

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.