#polynomials

Let $x_1$ and $x_2$ be the roots of $x^2+px+q=0$. Express $x_1^3+x_2^3$ in terms of $p$ and $q$ without solving the equation.

Find all polynomials $P$ with real coefficients such that $P(x^2)=P(x{)}^2$ for every real $x$.

Solve the system $x+y+z=6,xy+yz+zx=11,xyz=6.$