On the Number of Rational Roots of a Rational Polynomial

Abstract

We propose an extension of Gauss’s lemma and Schönemann-Eisenstein’s irreducibility criterion to determine the impossibility of decomposing an integer polynomial into several polynomials with rational coefficients. This extension allows us to obtain some limitations on the number of rational roots and on the degrees of the factors of a rational polynomial.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Acknowledgment

The authors wish to thank the referees for their helpful suggestions.

Additional information

Notes on contributors

Francesco Laudano

Francesco Laudano ([email protected]) received his Ph.D. in mathematics and physics from University of Salerno in 2018. He teaches mathematics at Pagano High School in Campobasso, Italy. Francesco’s research is mostly in elementary mathematics from an advanced standpoint. Apart from professional activities, he enjoys traveling with his wife Carmen and their sons Rosita and Mattia.