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Quadratic polynomial inequality

Source: Romanian TST 1979 Day 1 P4

April 15, 2023
algebraPolynomialspolynomialquadraticsinequalities

Problem Statement

Give an example of a second degree polynomial P∈R[x]P\in \mathbb{R}[x] such that ∀x∈R with ∣x∣⩽1:  ∣P(x)+1x−4∣⩽0.01.\forall x\in \mathbb{R}\text{ with } |x|\leqslant 1: \; \left|P(x)+\frac{1}{x-4}\right| \leqslant 0.01. Are there linear polynomials with this property?
Octavian Stănășilă
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