Geodesic
Geometric relations between the zeros of polynomials
Informatics and Automation, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 325-332.

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We consider the classical theorem of Grace, which gives a condition for a geometric relation between two arbitrary algebraic polynomials of the same degree. This theorem is one of the basic instruments in the geometry of polynomials. In some applications of the Grace theorem, one of the two polynomials is fixed. In this case, the condition in the Grace theorem may be changed. We explore this opportunity and introduce a new notion of locus of a polynomial. Using the loci of polynomials, we may improve some theorems in the geometry of polynomials. In general, the loci of a polynomial are not easy to describe. We prove some statements concerning the properties of a point set on the extended complex plane that is a locus of a polynomial. 
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     author = {Bl. Sendov},
     title = {Geometric relations between the zeros of polynomials},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2016_293_a20/}
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Bl. Sendov. Geometric relations between the zeros of polynomials. Informatics and Automation, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 325-332. http://geodesic.mathdoc.fr/item/TRSPY_2016_293_a20/

[1] Rahman Q.I., Schmeisser G., Analytic theory of polynomials, Oxford Univ. Press, Oxford, 2002 | MR | Zbl

[2] Sendov Bl., Sendov H., “Loci of complex polynomials. Part I”, Trans. Amer. Math. Soc., 366:10 (2014), 5155–5184 | DOI | MR | Zbl

[3] Sendov Bl., Sendov H., “Loci of complex polynomials. Part II: Polar derivatives”, Math. Proc. Cambridge Philos. Soc., 159:2 (2015), 253–273 | DOI | MR