Abstract
The Classical Grace’s Theorem is concerned with the relation between zeros of two apolar polynomials. The goal of this paper is to determine the relationship between zeros of two polynomials that are not apolar. As a result, we generalize both the Grace’s Theorem and a related result of A. Aziz also concerning apolar polynomials. Apart from this, we obtain an interesting result about the location of zeros of higher derivatives of a polynomial. We also prove a result that will give a region in which at least one critical point of a given polynomial lies.
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References
Aziz, A.: On the zeros of composite polynomials: Pacific. J. Math. 103, 1–7 (1982)
Grace, J.H.: The zeros of a of polynomial. Proc Camb Philos Soc 11, 352–357 (1902)
Rahman, Q.I., Schmeisser, G.: Analytic Theory of Polynomials. Oxford University Press (2002)
Rather, N.A., Ibrahim, M.: Generalization of the Grace Theorem. J. Indian Math. Soc. 84, 01–03 (2017)
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Mir, M.I., Nazir, I. & Wani, I.A. Relation between zeros of polynomials. Bol. Soc. Mat. Mex. 29, 13 (2023). https://doi.org/10.1007/s40590-022-00486-9
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DOI: https://doi.org/10.1007/s40590-022-00486-9