vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2024-60-4-280-294vestifm-808Research ArticleМАТЕМАТИКАMATHEMATICSАнализ корней триномиальных полиномовAnalysis of roots of trinomial polynomialsЧернявскийМ. М.ChernyavskyM. M.

Чернявский Михаил Михайлович – старший преподаватель кафедры инженерной физики

пр. Московский, 33, 210038, Витебск

Mikhail M. Chernyavsky – Senior Lecturer at the Department of Engineering Physics

33, Moskovskii Ave., 210038, Vitebsk

misha360ff@mail.ruВитебский государственный университет имени П. М. МашероваVitebsk State University named after P. M. Masherov202408012025604280294Copyright © Чернявский М.М., 20252025Чернявский М.М.Chernyavsky M.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/808

Разработан простой и единообразный метод, позволяющий устанавливать число и локализацию действительных решений трехчленных (триномиальных) алгебраических уравнений произвольной степени с действительными коэффициентами. Метод основан на том, что при помощи определенных подстановок трехчленное уравнение приводится к уравнению с одним параметром, представимым в виде явной функции от коэффициентов первоначального уравнения, и свойства решений исходного уравнения зависят только от значений этого параметра.

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.

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The authors declare that there are no conflicts of interest present.