Challenge problem:

Given:

1) $\displaystyle x^2-2ax+b=0$ with $\displaystyle b\neq 0$

2) $\displaystyle |x_{2}|< |x_{1}|$,where $\displaystyle x_{1},x_{2}$ are the roots of the above equation

Prove:

$\displaystyle 2(2a^2-b)-|b|< x_{1}^2<2(2a^2-b)$

Moderator approved, CB