A regra dos sinais de Descartes

Abstract

In this work, we study the Rule Signs of Descartes, which was conjectured by him in the mid-seventeenth century, where it linked the number of positive roots of a polynomial with the signs of their coeficients. Initially, we will present a statement of Descartes elaborated by Xiaoshen Wang [8]. Then we will study a similar rule for more general functions, whose statement was made by Vilmos Komornik [7]. Finally, we will bring a Roadmap on how to approach the subject in schools, along with a list of xed and commented exercises involving the theme.