Problem

Source: Romanian TST 1979 Day 1 P4

Tags: algebra, Polynomials, polynomial, quadratics, inequalities



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