Roots of quadratic equation

Question

If the roots of $ax^2+bx+c$ are $\alpha$ and $\beta$, express $\frac1\alpha-\frac1\beta$ in terms of $a$, $b$ and $c$.

I know how to express $\alpha+\beta$ or $\alpha\beta$ which is usually enough, but this question requires $\alpha-\beta$ to solve it. How do I proceed?

Answer 1

Hint:

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

Answer 2

You can find the roots of the polynomial from the quadratic equation, so you have your alpha and beta