Question 31
Let $x^2 - p_i x + q_i = 0$, $i = 1, 2, \dots, 15$ be 15 quadratic equations, where each of the $p_i$ and $q_i$, $i = 1, 2, \dots, 15$ is one of the numbers $1, 2, \dots, 30$, with no repetition nor omission. Determine the maximum possible number of real roots among the equations which are of values greater than 20.