Description of Some Methods of Solving Third and Fourth Degree Algebraic Equations in One Variable: a historical review Descripci ´on de algunos m´etodos de soluci´on de ecuaciones algebraicas de tercer y cuarto grado en una variable: una rese ˜ na hist ´orica

Abstract

The aim of the present work is to make a detailed exposition of the solution by radicals of equations of degree three and four in one variable, using different methods. In the case of the third degree equation, the methods of Niccolo Fontana (Tartaglia) and Girolamo Cardano are described, who were the ones who gave the solution of this equation, with positive coefficients. The general equation of third degree equation, i.e. with real coefficients, is also given and the method for finding all the real and complex solutions is detailed. The method of Franc¸ois Vi`ete, for a particular case of the equation of degree three, is also described. For the fourth degree equation with real coefficients, the method of Ludovico Ferrari and the method of Ren´e Descartes are described. In addition, the methods are illustrated with detailed examples.