Discriminantes de equações com uma variável

Abstract

Since ancient times, with the discoveries of papyrus and clay tablets, the study of algebra and, above all, the science of equations, have become great challenges for extraordinary mathematical scholars. Throughout history, several algebraic concepts and nomenclatures emerged. In the 2nd and 3rd degree equations, for example, we come across the so-called discriminant of equations and we calculate it, this is the object of study of this research. The present dissertation consists, then, in verifying the nature of the roots of equations according to values assumed by their discriminant, starting with particular cases. It is analyzed when an integer can be the value of a quadratic equation discriminant with all its integer coefficients; the discriminant is represented as a function of the roots of 2nd and 3rd degree equations, specifically, and in general, the discriminant is related to the roots of degree equations. The discriminant is also related as a function of the equations coefficients, making a connection with polynomial results and Sylvester Matrix, where its concepts are explored.