Roots of Pell-Lucas polynomials

Abstract

In this paper, we consider the Pell-Lucas polynomials. We express these poly- nomials as complex hyperbolic functions. Using this we obtain general root formula for Pell-Lucas polynomials. Furthermore, we give some interesting identities about images of roots of a polynomial under another member of the family. Finally, we get some amazing relationships between the roots of Pell-Lucas polynomials and the modular group, Hecke groups, generalized Hecke groups with geometric viewpoints.