NL-NWO 1988 Problem 1

The real numbers $x_1,x_2,..., x_n$ and $a_0,a_1,...,a_{n-1}$ with $x_i \ne 0$ for $i \in\{1,2,.., n\}$ are such that $$(x-x_1)(x-x_2)...(x-x_n)=x^n+a_{n-1}x^{n-1}+...+a_1x+a_0$$ Express $x_1^{-2}+x_2^{-2}+...+ x_n^{-2}$ in terms of $a_0,a_1,...,a_{n-1}$ .