MathNet 2022-part-05 — 197 problems (EN–VI) Question 7

Let $p$ and $q$ be distinct primes. For how many different values of $a$ are both solutions of the quadratic equation $x^{2}+a x+p q=0$ integers?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0