Aspectos históricos e matemáticos da resolução de equações de 3o., 4o. e 5o. graus

Abstract

During the years from 1530 to 1576, there were great mathematical advances in Europe, one of the greatest being the great duel of the resolution of the cubic equations, fought between Niccolò Tartaglia and Gerolamo Cardano, which brought Cardano renown and Tartaglia disgrace. The then formula for solving the cubic equations, like its history, is part of a long duel, in which there is a great friendship and a turning point of a publication that had been promised to remain secret. Even though Tartaglia and Cardano solved only 3rd degree equations, Ferrari developed a method for solving 4th degree equations, and with the help of derivatives we can solve almost all polynomial equations up to 5th degree.