AMC 12B 2004 Problem 17

For some real numbers a and b, the equation

8 x^{3}+4 a x^{2}+2 b x+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 ?

Answer Choices
A. -256
B. -64
C. -8
D. 64
E. 256