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?
Let the roots be x, y , z
So
[ log 2 x + log 2 y + log 2 z ] = 5
log 2 (xyz) = 5
2^5 = xyz
xyz = 32
And the product of the roots = -a/ 8
xyz = -a / 8
32 = -a / 8
256 = - a
a = -256
