Finding coefficients of cubic with roots in geometric series

[MegaDeth]

1. Homework Statement

x^3 +px^2 + 56x + q = 0


I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given.

2. Homework Equations

Given that the three roots are all positive and are the first free terms of a geometric series with common ratio 2,

a. find the three roots of the equation.

b. find the values of p and q.


3. The Attempt at a Solution

I've work out the old roots,

roots one at a time = -p

roots two at a time = 56

product = -q

 

[micromass]

The most important piece of information here is that the three roots are part of a geometric sequence with factor 2.

What is a geometric sequence with factor 2?? What is the formula?? How can you express an element with respect to a previous element??