Descartes' Rule of Signs by an Easy Induction

2007/10/09 by Arthan, R. D.
#26C #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.0710.1881

Abstract

If c is a positive number, Descartes' rule of signs implies that multiplying a polynomial f(x) by c - x introduces an odd number of changes of sign in the coefficients. We turn this around, proving this fact about sign changes inductively and deriving Descartes' rule from it.

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