Equações polinomiais: as fórmulas clássicas e a resolubilidade por meio de radicais

• Ano de defesa: 2014
• Autor(a) principal: Almeida, Taís Ribeiro Drabik de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Tecnológica Federal do Paraná; Curitiba; Mestrado Profissional em Matemática em Rede Nacional
• Palavras-chave em Português: 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
• Link de acesso: http://repositorio.utfpr.edu.br/jspui/handle/1/796

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.