A Proof of Descartes’ Rule of Signs

Authors

  • Antonio Fontana Liceo Scientifico “G. Mercalli”, Naples, Italy

DOI:

https://doi.org/10.23755/rm.v35i0.425

Keywords:

roots of a polynomial, derivative of a polynomial

Abstract

In 1637 Descartes, in his famous Géométrie, gave the rule of the signs without a proof. Later many different proofs appeared of algebraic and analytic nature. Among them in 1828 the algebraic proof of Gauss. In this note we present a proof of Descartes’ rule of signs that uses the roots of the first derivative of a polynomial and that can be presented to the students of the last year of a secondary school.

References

Descartes, R. (1637). La géometrie (Discours de la méthode, third part), Ed. of Leyde, 373.

Gauss, C. F. (1828). Beweis eines algebraischen Lehrsatzes, Crelle’s Journal fur die reine und ange-wandte Mathematik, 3(1).

Segner, J. A. (1728) Dissertatio epistolica, qua regulam Harriotti,

University of Jena.

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Published

2018-12-31

Issue

Vol. 35 (2018)

Section

Volume 35-2018

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