A regra dos sinais de Descartes

Detalhes bibliográficos
Autor(a) principal: COUTINHO, Adriano Chagas
Data de Publicação: 2016
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Biblioteca Digital de Teses e Dissertações da UFRPE
Texto Completo: http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7905
Resumo: In this work, we study the Rule Signs of Descartes, which was conjectured by him in the mid-seventeenth century, where it linked the number of positive roots of a polynomial with the signs of their coeficients. Initially, we will present a statement of Descartes elaborated by Xiaoshen Wang [8]. Then we will study a similar rule for more general functions, whose statement was made by Vilmos Komornik [7]. Finally, we will bring a Roadmap on how to approach the subject in schools, along with a list of xed and commented exercises involving the theme.
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spelling GOMES JUNIOR, Antonio José FerreiraGOMES JUNIOR, Antonio José FerreiraDUQUE, Karla Ferreira de ArrudaMACEDO, Ricardo Burity CrocciaCOUTINHO, Adriano Chagas2019-04-01T13:37:30Z2016-08-25COUTINHO, Adriano Chagas. A regra dos sinais de Descartes. 2016. 42 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife.http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7905In this work, we study the Rule Signs of Descartes, which was conjectured by him in the mid-seventeenth century, where it linked the number of positive roots of a polynomial with the signs of their coeficients. Initially, we will present a statement of Descartes elaborated by Xiaoshen Wang [8]. Then we will study a similar rule for more general functions, whose statement was made by Vilmos Komornik [7]. Finally, we will bring a Roadmap on how to approach the subject in schools, along with a list of xed and commented exercises involving the theme.Neste trabalho, estudaremos a Regra dos Sinais de Descartes, que foi conjecturada por ele em meados do século XVII, onde o mesmo relacionou o número de raízes positivas de um polinômio com os sinais de seus coe cientes. Inicialmente, apresentaremos uma demonstração do resultado de Descartes elaborada por Xiaoshen Wang [8]. Em seguida, estudaremos uma regra parecida para funções mais gerais, cuja demonstração foi feita por Vilmos Komornik [7]. Para nalizar, traremos um Roteiro de como abordar o assunto nas escolas, juntamente com uma lista de exercícios resolvidos e comentados, envolvendo o tema.Submitted by Mario BC (mario@bc.ufrpe.br) on 2019-04-01T13:37:30Z No. of bitstreams: 1 Adriano Chagas Coutinho.pdf: 428202 bytes, checksum: 30270e650b9d9b32e97511989d78ebc2 (MD5)Made available in DSpace on 2019-04-01T13:37:30Z (GMT). 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dc.title.por.fl_str_mv A regra dos sinais de Descartes
title A regra dos sinais de Descartes
spellingShingle A regra dos sinais de Descartes
COUTINHO, Adriano Chagas
Regra dos sinais de Descartes
Ensino de matemática
Resolução de problemas
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short A regra dos sinais de Descartes
title_full A regra dos sinais de Descartes
title_fullStr A regra dos sinais de Descartes
title_full_unstemmed A regra dos sinais de Descartes
title_sort A regra dos sinais de Descartes
author COUTINHO, Adriano Chagas
author_facet COUTINHO, Adriano Chagas
author_role author
dc.contributor.advisor1.fl_str_mv GOMES JUNIOR, Antonio José Ferreira
dc.contributor.referee1.fl_str_mv GOMES JUNIOR, Antonio José Ferreira
dc.contributor.referee2.fl_str_mv DUQUE, Karla Ferreira de Arruda
dc.contributor.referee3.fl_str_mv MACEDO, Ricardo Burity Croccia
dc.contributor.author.fl_str_mv COUTINHO, Adriano Chagas
contributor_str_mv GOMES JUNIOR, Antonio José Ferreira
GOMES JUNIOR, Antonio José Ferreira
DUQUE, Karla Ferreira de Arruda
MACEDO, Ricardo Burity Croccia
dc.subject.por.fl_str_mv Regra dos sinais de Descartes
Ensino de matemática
Resolução de problemas
topic Regra dos sinais de Descartes
Ensino de matemática
Resolução de problemas
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this work, we study the Rule Signs of Descartes, which was conjectured by him in the mid-seventeenth century, where it linked the number of positive roots of a polynomial with the signs of their coeficients. Initially, we will present a statement of Descartes elaborated by Xiaoshen Wang [8]. Then we will study a similar rule for more general functions, whose statement was made by Vilmos Komornik [7]. Finally, we will bring a Roadmap on how to approach the subject in schools, along with a list of xed and commented exercises involving the theme.
publishDate 2016
dc.date.issued.fl_str_mv 2016-08-25
dc.date.accessioned.fl_str_mv 2019-04-01T13:37:30Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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status_str publishedVersion
dc.identifier.citation.fl_str_mv COUTINHO, Adriano Chagas. A regra dos sinais de Descartes. 2016. 42 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife.
dc.identifier.uri.fl_str_mv http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7905
identifier_str_mv COUTINHO, Adriano Chagas. A regra dos sinais de Descartes. 2016. 42 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife.
url http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7905
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dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática (PROFMAT)
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