Equações polinomiais de até quarto grau: o limite das soluções gerais por radicais

Abstract

Trying to enrich the Maths teaching, discussion about techniques and equation solutions of up to fourth degree became the subject of this work, focusing on these sentences resolutions through radicals. In order to analize the main techniques which lead to the solution of polynomial equations through radicals, was explored a theoretical contribution on polynomials, complex numbers, able to promote understanding of the techniques used throughout history such as Girards Relations, the Solving Formula of a Quadratic Equation and the methods of: Viète, Carnado and Ferrari. In addition, was investigated the limitations of some methods for several situations and were very important for the production and revision of a part of our mathematical literature, including a modest approach to Galois history and theory. This works development also provided a brief investigation of why some methods are so little known when compared to others, leaving us the impression that the excesses of prerequisites and the elaborate algebraic language are sources that help to their being, in part, forgotten in time.