A new look at third degree equations
DOI:
https://doi.org/10.35819/remat2023v9i1id6252Keywords:
Third degree equations, Third degree polynomials, Roots, FormulaAbstract
In this article, we develop an explanation about the third degree equations (or alternatively, cubic equations) and third degree polynomials, presenting a new relationship between their respectives roots, described by a closed formula that, in terms of one simple root, allows us to express other roots. We must emphasize that this formula enables the introduction of a new discriminant. Consequently, we obtain criteria to identify the number of real and non-real complex roots of third degree equations and polynomials, as well as their multiplicities.
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BOYER, C. B. História da Matemática. 3. ed. São Paulo: Edgard Blücher, 2012.
GONÇALVES, A. Introdução à Álgebra. 5. ed. Rio de Janeiro: IMPA, 2013.
LIMA, E. L. Equação do terceiro grau. Matemática Universitária, n. 5, p. 9-23, jun. 1987. Disponível em: https://rmu.sbm.org.br/wp-content/uploads/sites/27/2018/03/n05_Artigo01.pdf. Acesso em: 29 jun. 2023.
LIMA, E. L.; CARVALHO, P. C. P.; WAGNER, E.; MORGADO, A. C. A Matemática do Ensino Médio. v. 1. 10. ed. Rio de Janeiro: SBM, 2012.
PEREIRA, O. E. S. Raízes de Equações do Terceiro Grau. 2017. 34 f. Monografia (Curso de Ciências da Natureza e Matemática) - Instituto de Ciências Exatas e da Natureza, Universidade da Integração Internacional da Lusofonia Afro-Brasileira, Redenção, 2017.
RUGGIERO, M. A. G.; LOPES, V. L. R. Cálculo Numérico: Aspectos Teóricos e Computacionais. 2. ed. São Paulo: Makron Books, 1997.
SILVA FILHO, J. F.; PEREIRA, O. E.; CASTRO, F. C. S. Simplificando a Resolução da Equação do Terceiro Grau. Professor de Matemática Online, v. 10, n. 4, p. 440-453, 2022. DOI: https://doi.org/10.21711/2319023x2022/pmo1031.
SILVA FILHO, J. F.; PEREIRA, O. E. Revisitando as Equações do Terceiro Grau. Professor de Matemática Online, v. 7, n. 2, p. 205-214, 2019. DOI: https://doi.org/10.21711/2319023x2019/pmo716.
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https://orcid.org/0000-0002-0893-7426
