Rational expressions for multiple roots of polynomials
https://doi.org/10.29235/1561-8323-2025-69-2-95-100
Abstract
For polynomials possessing multiple roots we deduce explicit formulas for higher derivatives of resultants R(f, f (k)) (f (k) is a derivative of order k). On this basis a number of results linking higher derivatives of resultants and multiple roots of polynomials that differ in ideas from the well-known ones are obtained.
Supporting agencies: The study was carried out with financial support from the Belarusian Republican Foundation for Fundamental Research (project Ф23М-003).
About the Author
M. M. Chernyavsky
Vitebsk StateUniversity named after P. M. Masherov
Belarus
Belarus
Chernyavsky Mikhail M. – Lecturer
33, Moskovskiy Ave., 210038, Vitebsk
References
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4. Chernyavsky M. M., Trubnikov Yu. V. Modification of Aitken’s formulas and algorithms for analytical finding of multiple roots of polynomials. Vesnіk Vіtsebskaga dzyarzhaunaga unіversіteta = Bulletin of Vitebsk State University, 2021, no. 1 (110), pp. 13–25 (in Russian).
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