Let D¯ denote the unit disk {z : |z| < 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¯.
@article{bwmeta1.element.doi-10_2478_v10062-012-0025-x,
author = {Somjate Chaiya and Aimo Hinkkanen},
title = {Location of the critical points of certain polynomials},
journal = {Annales UMCS, Mathematica},
volume = {67},
year = {2013},
pages = {1-9},
zbl = {1295.30016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0025-x}
}
Somjate Chaiya; Aimo Hinkkanen. Location of the critical points of certain polynomials. Annales UMCS, Mathematica, Tome 67 (2013) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0025-x/
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