Polynomials that have Golden Ratio Zeros
Publication Date
January 2014
Abstract
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.
Disciplines
Mathematics
Recommended Citation
He, Tian-Xiao; Maier, Jack; and Vanness, Kurt, "Polynomials that have Golden Ratio Zeros" (2014). Scholarship. 25.
https://digitalcommons.iwu.edu/math_scholarship/25