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max of (a - b)(2a - b)}/a(a - b + c) when ax^2 + bx + c = 0 has roots in [0, 1]

Source: 2013 Saudi Arabia Pre-TST 2.2

September 13, 2020

algebramaxquadratic polynomial

Problem Statement

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)}