A Reciprocal Coefficient Product

★ 9/10Absolute Value algebra Polynomials inequality

Problem

Let $f(x) = ax^2 + bx + c$ and $g(x) = cx^2 + bx + a$ , and set

F(x) = |f(x)g(x)|, \qquad x \in [-1, 1].

If $|g(x)| \leqslant 1$ for all $x \in [-1, 1]$ , find the maximum possible value of $F(x)$ .

Answer

Solution

Difficulty	9/10
Topics	Absolute Value, algebra, Polynomials, inequality

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