Solução de equações polinomiais por meio de radicais

Abstract

For many years, mathematicians have dedicated to nding solutions for eventual problems. One of those that intrigued them, it was the solution of equations. As a result of these studies, today we have formulas that solve any polynomial equation of degree 4. However, when the challenges came to be about equations of degree 5. It was concluded that it was not always possible to nd solutions expressed by radicals. Many mathematicians have dedicated to solve this problem. Josefh Louis Lagrange in 1770 found that the gimmicks used in the equations of degrees 3 and 4 did not t for degrees 5. They suspected that it might not always be possible to determine the solutions. In 1824, the mathematician, Niels Henrik Abel was able to prove these suspicious. But it stayed the question: When would it be possible to nd solutions of radicals for equations of degree 5? And in 1843, the mathematician Evariste Galois' brilliant work came to the Paris Academy of Sciences, who developed the important theory that bears his name, as well as the Group Theory, which beautifully explains this question. We will do an introductory study of Group Theory, Field Extensions, and Galois Theory, which it will serve as tools for showing \the solution of polynomial equations through radicals".