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.

Author Bio

Thomas Polstra graduated from Georgia State University in Spring of 2012. He will be attending the University of Missouri for a PhD in Mathematics. His main mathematical interests lie in Commutative Algebra and Real Analysis. This research was performed as part of the 2010-2011 RIMMES (Research in Mathematics, Mathematics Education, and Statistics) program at Georgia State University.