Estudo geométrico das equações do terceiro e quarto graus

Abstract

In this work we studied the third and fourth degree equations from a geometric point of view. We show how, in a certain sense, the roots of a cubic equation are associated with the vertices of an equilateral triangle circumscribed to a circle whose radius is a function of the coefficients of such an equation and how the roots of a quartic equation are associated with the abscissa of four points on a circle whose radius is a function of the coefficients of the equation. In the work we present all the necessary arguments to understand these problems and conclude by showing how from such constructions we can obtain a procedure that, with the help of a scientific calculator, gives us the roots of a specific quartic equation, which has two positive real roots and two negative real roots.