It has been conjectured by Casas-Alvero that polynomials of degree n over fields of characteristic 0, share roots with each of its n-1 derivatives if and only if those polynomials have one root of degree n. In this paper, using the analytic theory of polynomials, an equivalent formulation of the Casas-Alvero Conjecture is established for polynomials over the complex plane t ogether with several special cases of it.
"Convex Hulls and the Casas-Alvero Conjecture for the Complex Plane,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 13
, Article 2.
Available at: http://scholar.rose-hulman.edu/rhumj/vol13/iss1/2