The quadratic equation $ax^2 + bx + c = 0$ has its roots in the interval $[0, 1]$. Find the maximum of $\frac{(a - b)(2a - b)}{a(a - b + c)}$.
Source: 2013 Saudi Arabia Pre-TST 2.2
Tags: algebra, max, quadratic polynomial
The quadratic equation $ax^2 + bx + c = 0$ has its roots in the interval $[0, 1]$. Find the maximum of $\frac{(a - b)(2a - b)}{a(a - b + c)}$.