Analysis of roots of trinomial polynomials
https://doi.org/10.29235/1561-2430-2024-60-4-280-294
Abstract
In the article we develop a simple and uniform method that allows one to calculate the number and localization of real solutions of three-term (trinomial) algebraic equations of arbitrary degree with real coefficients. The method is based on the fact that using certain substitutions, a three-term equation is reduced to an auxiliary equation with one parameter, represented as an explicit function of the coefficients of the initial equation, and the properties of the solutions of the initial equation depend only on the values of this parameter.
Supporting agencies: The research was carried out with financial support from the Belarusian Republican Foundation for Fundamental Research (grant no. 20231184) and in the framework of the State Program of Scientific Research “Convergence2025” (task no. 20210494).
About the Author
M. M. Chernyavsky
Vitebsk State University named after P. M. Masherov
Belarus
Belarus
Mikhail M. Chernyavsky – Senior Lecturer at the De
partment of Engineering Physics
33, Moskovskii Ave., 210038, Vitebsk
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