Question 14
The real numbers $r_{1}, r_{2}, \ldots, r_{2019}$ satisfy the conditions $r_{1}+r_{2}+\ldots+r_{2019}=0$ and $r_{1}^{2}+r_{2}^{2}+\ldots+r_{2019}^{2}=1$. Let $a=\min \left(r_{1}, r_{2}, \ldots, r_{2019}\right)$ and $b=\max \left(r_{1}, r_{2}, \ldots, r_{2019}\right)$. Prove: $a b \leq \frac{-1}{2019}$.