Equações polinomiais: as fórmulas clássicas e a resolubilidade por meio de radicais
The solvability by radicals of polynomial equations with rational coefficients is an important part of the history of algebra. The problem was to express a root by means of basic arithmetic operations and radicals. Formulas to solve polynomial equations of degree lower than or equal to 4 were obtain...
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| Formato: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Brasil |
| Recursos: | Universidade Tecnológica Federal do Paraná (UTFPR) |
| Repositorio: | Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT)) |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.utfpr.edu.br:1/796 |
| Acesso em linha: | http://repositorio.utfpr.edu.br/jspui/handle/1/796 |
| Access Level: | acceso abierto |
| Palavra-chave: | Equações - Soluções numéricas Polinômios Galois, Teoria de Teoria dos grupos Álgebra Matemática - Estudo e ensino Matemática Equations - Numerical solutions Polynomials Galois theory Group theory Algebra Mathematics - Study and teaching Mathematics |
| Resumo: | The solvability by radicals of polynomial equations with rational coefficients is an important part of the history of algebra. The problem was to express a root by means of basic arithmetic operations and radicals. Formulas to solve polynomial equations of degree lower than or equal to 4 were obtained in XVIth century. About three centuries later, Niels Abel showed that it is not possible to find a formula for the general equation of degree 5. Finally, Evariste Galois solved the problem by studying the permutations groups, establishing the exact conditions for the solvability of a polynomial equation. In this work we present a brief history of the classic formulas for the roots of equations with degree lower or equal to 4. Then we study solvability by radicals of polynomial equations of degree higher than or equal to 5. |
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