RU-SPB 2008 Problem 3

There are $2008$ trinomials $x^2-a_kx+b_k$ where $a_k$ and $b_k$ are all different numbers from set $(1,2,...,4016)$ . These trinomials has not common real roots. We mark all real roots on the $Ox$ -axis. Prove, that distance between some two marked points is $\leq \frac{1}{250}$