Polynomials that have Golden Ratio Zeros

Publication Date

January 2014


When the golden ratio and its conjugate are zeros to a polynomial, two of the coefficients are functions of the Fibonacci sequence in terms of the other coefficients, which characterize the polynomial completely. These functions are used to derive some Fn, Ln, and golden ratio identities. In many cases, this is generalized to the Lucas sequences Un and Vn, with an associated quadratic root pair. Horadam sequences are produced in the series of linear and constant coefficients of the series of polynomials Having ra and rb zeros when all of the other coefficients are equal.