TH-TMO 2013 Problem 4

Determine all monic polynomials $p(x)$ having real coefficients and satisfying the following two conditions: $\bullet$ $p(x)$ is nonconstant, and all of its roots are distinct reals $\bullet$ If $a$ and $b$ are roots of $p(x)$ then $a + b + ab$ is also a root of $p(x)$ .