Análise do discriminante em equações polinomiais de terceiro grau a partir de funções simétricas

• Autor(a) principal: Costa, Debora Naiure Araujo
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000005bfq
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/10985
• topic: Polinômios; Equações polinomiais; Funções simétricas das raízes; Discriminante; Polynomials; Polynomial equations; Symmetric root functions; Discriminant; CIENCIAS EXATAS E DA TERRA::MATEMATICA

The objective of this work is to make a study on the characteristics of the roots of polynomial equations of degrees 2 and 3, studying the discriminant written in function of invariants that depend only on the coefficients of an initial equation. We will start by remembering some important definitions and propositions about polynomials, symmetric functions of the roots and develop the resolution of the cubic by radicals using two different methods. Finally, it will be possible to analyze the discriminant through algebraic manipulations that we will do, using the content presented in the previous chapters, and then we will write the discriminant from the roots of the equations, which enable to develop a proof for the theorems that relate the roots of the equations 2º and 3º degrees with their discriminants.