Roots of quadratic equations.

I've made it to the last question on a homework piece, but I just can't figure out how to start. The question is -

One root of the equation x² - px + q = 0 is twice the other root. Show that 2p² = 9q.

Originally, I just re-arranged 2p²=9q to p=(sqrt)9q/2, and subbed in some numbers, until I got p=4.5, q=9. But my maths tutor said that's not the answer he's looking for, and that I should be using alpha and beta, and to try again tonight. I've spent the last 45 mins scribbling bits out to no avail, I just don't know how to get the values of alpha and beta to prove 2p²=9q.

Any suggestions?