MathNet 2016-part-05 — 184 problems (EN–VI) Question 99

Let $P(x)$ and $Q(x)$ be quadratic polynomials with rational coefficients and assume that the roots of $P(x)$ are irrational numbers $a$ and $b$. If $a + 2016$ is one of the roots of $Q(x)$, find all possible values for the other root.