Geodesic
Location of the critical points of certain polynomials
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 67 (2013) no. 2 Cet article a éte moissonné depuis la source Library of Science

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Let 𝔻 denote the unit disk {z:|z| lt;1} in the complex plane ℂ. In this paper, we study a family of polynomials P with only one zero lying outside 𝔻.  We establish  criteria for P to satisfy implying that each of P and P'  has exactly one critical point outside 𝔻.
Keywords: Polynomial, critical point, anti-reciprocal. 
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Chaiya, Somjate; Hinkkanen, Aimo. Location of the critical points of certain polynomials. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 67 (2013) no. 2. http://geodesic.mathdoc.fr/item/AUM_2013_67_2_a3/

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