Roots of trinomial and quadrinomial equations

Author(s)

Jéssica Ventura da Silva

• Document type: Master's Dissertation
• Press: Presidente Prudente. 2018-03-13.
• Institution: Universidade Estadual Paulista (Unesp). Faculdade de Ciências e Tecnologia. Presidente Prudente
• Defense date: 2018-02-23
• Advisor: Vanessa Avansini Botta Pirani

Abstract

In order to determine the behavior of the roots of some kinds of trinomial equations, which appear in certain problems related to Financial Mathematics, this work presents the study of classical results that determine regions of the complex plane where the zeros of a given polynomial are located, as well as the study of specific results on the distribution of the roots of trinomial equations in the complex plane, according to their arguments and modules. Since the large application of the results on trinomials is related to the determination of the interest rate I of a uniform series of payments, this work also presents the study of financial functions involving compound interest. Then using all presented theory, we determine an annular region of the complex plane where are located the roots of the trinomial and quadrinomial equations related to the determination of the interest rate I. Furthermore we show, under certain conditions, that the roots of the trinomial equations are simple and we determine the sectors of the complex plane that contain exactly one root of these trinomial equations. (AU)

• FAPESP's process: 15/23752-3 - Roots of trinomial equations
• Grantee: Jéssica Ventura da Silva
• Support Opportunities: Scholarships in Brazil - Master