Sequences and series If $p, q, r$ are in G.P. and the equations:
$$px^2 + 2qx + r = 0$$ $$dx^2 + 2ex + f = 0$$
Have a common root, then show that 
$$\frac{d}{p}, \frac{e}{q}, \frac{f}r$$
are in A.P.
Well I tried taking the sum and products of the root, but that didn't get me anywhere. I was told that there is an extremely short way of doing this problem. Can anyone help me?

HINT:
As  $\displaystyle\frac qp=\frac rq, pr=q^2$
The roots of the first equations are $$x=\frac{-2q\pm\sqrt{4q^2-4pr}}{2p}=-\frac qp$$
Set this value in the second and replace $q^2$ with $pr$
