Resumen de Ecuaciones algebraicas y soluciones racionales.

Jesús Álvarez Mesa

• It is known that rational explicit solutions of an algebraic equation of two unknown factors, if they do exist, will depend on a rational parameter. For this, some existence conditions will have to be fullfilled. Otherwise, there will not be any rational solution. This is what happens with a certain family of equations related to a known theorem that are studied in this work. In addition to this, an algebraic equation with three unknown factors is also solved, and all the rational solutions are obtained and their corresponding geometric interpretation is given.