MathNet 2019-part-05 — 184 problems (EN–VI) Question 145

Two monic quadratic trinomials $f(x)$ and $g(x)$ are given, each of them has two distinct real roots. Assume that $f(1) = g(2)$ and $g(1) = f(2)$. Find all possible values of the sum of all four roots of the trinomials.