##### Title: Geometry of a Class of Generalized Cubic Polynomials

##### Pages: 93-99

##### Cite as:

Christopher Frayer, Geometry of a Class of Generalized Cubic Polynomials, Int. J. Anal. Appl., 8 (2) (2015), 93-99.#### Abstract

This paper studies a class of generalized complex cubic polynomials of the form p(z)=(z-1)(z-r_1)^k(z-r_2)^k where r_1 and r_2 lie on the unit circle and k is a natural number. We completely characterize where the nontrivial critical points of p can lie, and to what extent they determine the polynomial. The main results include (1) a nontrivial critical point of such a polynomial almost always determines the polynomial uniquely, and (2) there is a `desert' in the unit disk in which critical points cannot occur.

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