Coefficients Reversed

★ 7/10Quadratic Equations Absolute Value algebra Polynomials inequality

Problem

Suppose $|ax^2 + bx + c| \le 1$ for all $x \in [-1, 1]$ . Prove that

\left|cx^2 + bx + a\right| \le 2 \qquad \text{for all } x \in [-1, 1].

Answer

Solution

Difficulty	7/10
Topics	Quadratic Equations, Absolute Value, algebra, Polynomials, inequality

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