
alphabeta
Supposing $\displaystyle ax^2 + bx +c = 0$ (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 ($\displaystyle \alpha + \beta$ ($\displaystyle b/a$), $\displaystyle \alpha\beta$ ($\displaystyle c/a$), $\displaystyle \alpha^2 + \beta^2$). All good; but then it says "without finding the values of $\displaystyle \alpha$ or $\displaystyle \beta$, find $\displaystyle \alpha  \beta$.
I'm wondering how to rearrange that to use only $\displaystyle \alpha + \beta$s and $\displaystyle \alpha\beta$s.
Any help would be greatly appreciated.

$\displaystyle \alpha\beta=\sqrt{(\alpha\beta)^2}=\sqrt{\alpha^2+\beta^22\alpha\beta}=\sqrt{(\alpha+\beta)^24\alpha\beta}$