  In this work we consider a given root of a family of n-degree polynomials as
a one-variable function that depends only on the independent term. Then we
prove that this function satisfies several ordinary differential equations
(ODE). More concretely, it satisfies several simple separated variables ODE, a
first order generalized Abel ODE of degree n-1 and an (n-1)-th order linear
ODE. Although some of our results are not new, our approach is simple and
self-contained. For n=2, 3 and 4 we recover, from these ODE, the classical
formulas for solving these polynomials.
