AUSTRIAN-POLISH 1996 Problem 3

The polynomials $P_{n}(x)$ are defined by $P_{0}(x)=0,P_{1}(x)=x$ and $$P_{n}(x)=xP_{n-1}(x)+(1-x)P_{n-2}(x) n\geq 2$$ For every natural number $n\geq 1$ , find all real numbers $x$ satisfying the equation $P_{n}(x)=0$ .