1. ## |alpha-beta|

Supposing $ax^2 + bx +c = 0$ (this isn't actually the equation, but I'll have a better chance of understanding in general form):

I've been told to find the value of the usual root stuff ( $\alpha + \beta$ ( $-b/a$), $\alpha\beta$ ( $c/a$), $\alpha^2 + \beta^2$). All good; but then it says "without finding the values of $\alpha$ or $\beta$, find | $\alpha - \beta$|.

I'm wondering how to rearrange that to use only $\alpha + \beta$s and $\alpha\beta$s.

Any help would be greatly appreciated.

2. $|\alpha-\beta|=\sqrt{(\alpha-\beta)^2}=\sqrt{\alpha^2+\beta^2-2\alpha\beta}=\sqrt{(\alpha+\beta)^2-4\alpha\beta}$