If you look at what Mr. Fantastic gave you, he didn't include any beta. He used directly twice alpha instead of having alpha and beta.

If he used beta, then you'd have:

$\displaystyle (x - \alpha)(x - \beta) = x^2 - (\alpha + \beta) x + \alpha\beta$

Then;

$\displaystyle p = \alpha + \beta$

$\displaystyle q = \alpha\beta$

Then, you know that $\displaystyle \beta = 2\alpha$

This gives:

$\displaystyle p = \alpha + 2\alpha = 3 \alpha$

$\displaystyle q = \alpha(2\alpha) = 2\alpha^2$

Which comes back to what Mr. Fantastic gave you