A Proof of Descartes’ Rule of Signs
DOI:
https://doi.org/10.23755/rm.v35i0.425Keywords:
roots of a polynomial, derivative of a polynomialAbstract
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.
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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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