A Zero Times a Product

★ 8/10functions Quadratic Equations Completing the Square inequality

Problem

The function $f(x) = x^2 + ax + b$ (with $a, b \in \mathbb{R}$ ) has a zero $x_0$ in the interval $(0, 1]$ . Find the maximum value of

ab\left(\frac{x_0}{4} + \frac{1}{9x_0} - \frac{1}{3}\right).

Answer

Solution

Difficulty	8/10
Topics	functions, Quadratic Equations, Completing the Square, inequality

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