Aplicación de las Sustituciones de Descartes y Cardano para la Solución de Polinomios de Tercer y Cuarto Orden

Abstract

The substitutions here presented reduce the order of the polynomials with scalar coefficients. The cubic term of a fourth order canonical polynomial is eliminated by the Descartes-Cardan substitutions and reduced to a polynomial of order 3 by the Descartes substitutions. With the substitutions of Descartes-Tschirnhaus the quadratic term of the polynomial of degree 3 is eliminated, then it reduces to a polynomial of second degree, which is finally solved by the well-known general formula. The solution given by this general formula is known as the Cardano formula.