Os polinómios
Miniatura indisponível
Data
2018
Título da revista
ISSN da revista
Título do Volume
Editora
Edições Universitárias Lusófonas
Resumo
O presente artigo inicia-se evidenciando que os polinómios são entidades matemáticas de manuseamento muito fácil com aplicações práticas interessantes sendo, depois, feito o enquadramento dos polinómios no âmbito das expressões analíticas. No que respeita à determinação dos zeros dos polinómios são referidas as 1ª e 2ª regras de Descartes, a regra de Budan, a regra do máximo, o corolário do Teorema de Rolle e as relações de Newton. Depois as regras referidas são aplicadas à determinação dos zeros de polinómios de coeficientes inteiros, sendo evidenciada a seguinte ordem: zeros inteiros, zeros fracionários e zeros irracionais. Posteriormente é realçada a determinação de zeros de polinómios do 3º grau e, em notas finais, evidencia-se que, enquanto os polinómios dos 2º, 3º e 4º graus contemplam fórmulas resolventes genéricas que permitem expressar os seus zeros através de expressões racionais e de raízes de índice não superior ao grau do polinómio, o mesmo não sucede para polinómios de grau superior ao 4º sendo evidenciado que os méritos da demonstração desta realidade couberam a Niels Abel e a Evariste Galois.
In this paper we begin by highlighting that polynomials are mathematical entities with very interesting practical applications and it is also shown how they can be analysed within the framework of analytic expressions. To determine the zeros of a polynomial, we can use different mathematical results. Therefore, the first and second rules of Descartes, the Budan rule, the maximum rule, the corollary of Rolle’s Theorem, and Newton’s relations are presented. Those rules are then applied in the determination of the zeros of a polynomial with integer coefficients. We start by emphasize the determination of integer zeros, next the fractional zeros and finally the irrational zeros. Subsequently, the determination of zeros of a 3rd degree polynomial is explained, and in final notes, it is highlighted that there are formulas to find the zeros of a generic polynomial of 2nd, 3rd or 4th degree. However, the same does not happen for polynomials of degree higher than 4, as it was shown by Niels Abel and Evariste Galois.
In this paper we begin by highlighting that polynomials are mathematical entities with very interesting practical applications and it is also shown how they can be analysed within the framework of analytic expressions. To determine the zeros of a polynomial, we can use different mathematical results. Therefore, the first and second rules of Descartes, the Budan rule, the maximum rule, the corollary of Rolle’s Theorem, and Newton’s relations are presented. Those rules are then applied in the determination of the zeros of a polynomial with integer coefficients. We start by emphasize the determination of integer zeros, next the fractional zeros and finally the irrational zeros. Subsequently, the determination of zeros of a 3rd degree polynomial is explained, and in final notes, it is highlighted that there are formulas to find the zeros of a generic polynomial of 2nd, 3rd or 4th degree. However, the same does not happen for polynomials of degree higher than 4, as it was shown by Niels Abel and Evariste Galois.
Descrição
R-LEGO - Revista Lusófona de Economia e Gestão das Organizações
Palavras-chave
MATEMÁTICA , POLINÓMIOS, MATHEMATICS, POLYNOMIALS
Citação
Silva , A O F G D 2018 , ' Os polinómios ' , R-LEGO - Revista Lusófona de Economia e Gestão das Organizações .