algebra precalculus - How to find the value of this expression

Suppose I have a general quadratic equation $ax^2 + bx + c = 0$

And I have $\alpha , \beta$ as roots, then what is the simplest way to find $(a\alpha + b)^{-2} + (a\beta + b)^{-2}$ ?

I know the formula for finding the sum and product of roots, but that doesn't helped me in finding the value.

Any good hint is welcomed.

Answer

Some assumptions:
$c, \alpha, \beta \neq 0$ (the answer will be a bit modified without these assumptions)

Since $\alpha$ is a root therefore
$$\begin{align*} a\alpha^2+b\alpha+c &=0\\ a\alpha+b & = \frac{-c}{\alpha}\\ \frac{1}{(a\alpha+b)^2} & = \frac{\alpha^2}{c^2} \end{align*}$$

Thus
$$\begin{align*} \frac{1}{(a\alpha+b)^2} + \frac{1}{(a\beta+b)^2}& = \frac{\alpha^2+\beta^2}{c^2}\\ &= \frac{(\alpha+\beta)^2-2\alpha\beta}{c^2} \end{align*}$$