O método de Cardano e sua aplicação no ensino médio
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Data
2014-08-15
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Universidade Federal de Goiás
Resumo
This work presents a study on the Cardano's method applied in 3rd degree polynomial
equations of the form x3 + px + q = 0; p; q 2 R and use in the classroom, the 3rd year
of high school, working with the procedure without the use of formula to determine a
root of 3rd degree polynomial equation. The application of this method searches enable
to students a relevant intellectual enrichment for future studies of the exact sciences.
In this work not used a diagnostic evaluation to analyse the level of understanding of
theme, only search to apply the procedure used by Cardano, in the classroom, and
especially present a demonstration of this procedure to an equation in the general
form of the 3rd degree. The study brings a historical approach of the resolutions of
the equations, after, a theoretical foundation for the study of polynomials, detaching
the theorems main, propositions and key de nitions for the study of the polynomial
functions. Moreover, detach the study of the characteristics of the roots of an equation
of the 3rd degree of analytical and graphical form, where we present an analytical
resolution for the 4th degree equations. However, we conclude that the application
of this study demonstrates that students have greater facility to nd a root of an
equation in the general form, as well as the other roots. Therefore, the procedure used
in classroom presents a method to nd at least one root of an equation of the 3rd
degree, without the use of formula.
Keywords
Descrição
Palavras-chave
Equações polinomiais, Polinômios e característica das raízes, Polynomial equations, Polynomial and characteristic roots
Citação
MELO, Claudio Umberto de. O método de Cardano e sua aplicação no ensino médio. 2014. 75 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2014.