The North Carolina Journal of Mathematics and Statistics

Geometry of a Family of Quartic Polynomials

Christopher Frayer, Lukas Smith

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

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References


@ARTICLE{GOCP,

AUTHOR = {C. Frayer, and M. Kwon, and C. Shafhauser, and J.A. Swenson},

TITLE = {The Geometry of Cubic Polynomials},

YEAR = {2014},

JOURNAL = {Math. Magazine},

VOLUME = {87},

NUMBER = {2},

PAGES = {113--124}

}

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number={2},

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author={C. Frayer, and L. Gauthier},

title={A Tale of Two Circles: Geometry of a Class of Quartic Polynomials},

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year={2018},

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}

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author={C. Frayer, and P. Thomson},

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journal={Pi Mu Epsilon Math Journal},

volume={Fall},

year={2020},

number={},

pages={},

}

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