CIIM 2018 Problem 2

Let $p(x)$ and $q(x)$ non constant real polynomials of degree at most $n$ ( $n > 1$ ). Show that there exists a non zero polynomial $F(x,y)$ in two variables with real coefficients of degree at most $2n-2,$ such that $F(p(t),q(t)) = 0$ for every $t\in \mathbb{R}$ .