Métodos para determinação de raízes de equações polinomiais : uma abordagem voltada para o ensino médio

• Ano de defesa: 2016
• Autor(a) principal: SANTOS, Diógenes Silva dos
• Orientador(a): SILVA, Thiago Dias Oliveira
• Banca de defesa: SILVA, Thiago Dias Oliveira, MACEDO, Ricardo Burity Croccia, NEVES, Rodrigo José Gondim
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal Rural de Pernambuco
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática (PROFMAT)
• Departamento: Departamento de Matemática
• País: Brasil
• Palavras-chave em Português: Polinômio; Equação algébrica; Ensino médio
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7906

The present work aims to study the polynomials and their algebraic equations. The central idea of this project is to produce a material that can serve as a support for teachers that will address this issue and also to interested students. In this research priorizarei develop defi nitions and theorems related to polynomials of the way it is taught in textbooks used in high school. To the extent possible I will use plain language to facilitate understanding. Here the reader will find the defi nitions of polynomials, their operating properties, concept of degree and divisibility of polynomials. I will present the Fundamental Theorem of algebra and its application in the demonstrations. As a result in the demonstrate several theorems that will help in resolutions of polynomial equations, such as the decomposition of polynomials, roots factors combined, Girard, Newton sums and reciprocal polynomials. Then I'll discuss the rational roots of polynomials with integer coeficients, plus some important results in the solutions of these equations. Finally, will be proposed for educational purposes, some exercises in order to solidify the matter presented.