Recursive polynomials define some initial conditions, a function of x to build upon those initial conditions, and some natural number n to stop at. The Fibonacci polynomials are a notable example, with several closed form expressions including one that describes the exact value of all roots, real and complex. The Golden polynomials are another notable example, that slightly tweaks the initial conditions of the Fibonacci polynomials.

In our research, sponsored in part by SURIEM 2020, we sought to generalize the behavior of Golden polynomials through an alternate definition. We utilized mathematical software, including MATLAB and Mathematica, to analyze patterns and root behavior of our generalized, Golden-like recursive polynomial. Our work has been presented at several venues, including

• UTRGV College of Sciences Annual Research Conference - 2020

• Joint Mathematics Meetings - 2021

• Nebraska Conference for Undergraduate Women in Mathematics - 2021