Question 26
Let $P(x) = x^{2020} + x + 2$, which has $2020$ distinct roots. Let $Q(x)$ be the monic polynomial of degree $\binom{2020}{2}$ whose roots are the pairwise products of the roots of $P(x)$. Let $\alpha$ satisfy $P(\alpha) = 4$. Compute the sum of all possible values of $Q\left(\alpha^{2}\right)^{2}$.