Question 170
Consider the polynomial $P(X) = a X^{2} + b X + c$, where $a, b, c \in \mathbb{R}$, $a \neq 0$, and let $x_{1}, x_{2}$ be the roots of this polynomial. Prove that if $a$ lies between $c$ and $b-c$, then the interval $(-1,1)$ can contain at most one of these roots.