Question 31
Determine all monic polynomials $p(x)$ with real coefficients satisfying the following properties:
1) $p(x)$ is nonconstant and all its roots are real and distinct;
2) if $a$ and $b$ are roots of $p(x)$, then so is $a + b + ab$.
1) $p(x)$ is nonconstant and all its roots are real and distinct;
2) if $a$ and $b$ are roots of $p(x)$, then so is $a + b + ab$.