Solve the roots of a cubic polynomial? I have had trouble with this question - mainly due to the fact that I do not fully understand what a 'geometric progression' is:
"Solve the equation $x^3 - 14x^2 + 56x - 64 = 0$" if the roots are in geometric progression.
Any help would be appreciated.

It means the roots are of the form $a, ar, ar^2$.
Here it is not too difficult to see that $2, 4, 8$ are ok, just look at the constant term, which is $- (a \cdot ar \cdot ar^2) = - (a r)^3$, and check that $2, 4, 8$ fit with the other coefficients
$$
14 = 2 + 4 + 8,
\qquad
56 = 2 \cdot 4 + 2 \cdot 8 + 4 \cdot 8.
$$
