Estudo da fórmula de Cardano–Tartaglia para a resolução de equações do terceiro grau

Abstract

Nowadays, little is said about polynomial equations of degree greater than two and, because of that, many students finish high school without knowing how to solve third-degree equations in its general form by some method, and let alone the fourth degree. In light of this situation, we note the importance of conducting a study on the Cardano–Tartaglia formula. This study aims to analyze the contributions of the Cardano-Tartaglia formula to the solving third-degree polynomial equations. To do so, we use a framework pertinent, such as Boyer (1996), Garbi (2010), Lima (1987) among others. We highlight the main definitions and some correlated results. We describe the history of discovery of the general method for solving third degree equations, citing the mathematicians who stood out in the process of obtaining and disseminating the formula of Cardano–Tartaglia and the influences of this formula on the historical evolution of Mathematics. We present the demonstration of the Cardano-Tartaglia formula and its application, in addition to the study on the relationship between the discriminant and the roots of the third degree equation. We show the relevance of this formula in solving third-degree polynomial equations, in the discovery of complex numbers and in the search for algebraic methods for solving equations of degree four or greater. We conclude this study with the Ferrari method for solving polynomial equations of the fourth degree, their demonstration and application.