Article

Geometry of a Family of Quartic Polynomials

Authors

• • Christopher Frayer
  • University of Wisconsin - Platteville
• • Lukas Smith
  • University of Wisconsin - Platteville

Abstract

For a fixed $\mathcal{A} \in \mathbb{C}$ with $|\mathcal{A}|=1$, this paper characterizes critical points of polynomials of the form $p(z)=(z-1)(z-\mathcal{A})(z-r_1)(z-r_2)$ with $|r_1|=|r_2|=1$.

Keywords: Geometry of Polynomials, critical points, Gauss-Lucas Theorem

How to Cite: Frayer, C. & Smith, L. (2021) “Geometry of a Family of Quartic Polynomials”, North Carolina Journal of Mathematics and Statistics. 7(1).