Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
Abstract
Let $P(z)=a_0 + a_1z + \dots + a_{n-1}z^{n-1}+z^n$ be a polynomial of degree $n.$ The Gauss-Lucas Theorem asserts that the zeros of the derivative $P^\prime (z)= a_1 + \dots +(n-1) a_{n-1}z^{n-2}+nz^{n-1},$ lie in the convex hull of the zeros of $P(z).$ Given a zero of $P(z)$ or $P^\prime (z),$ A. Aziz [1], determined regions which contain at least one zero of $P(z)$ or $P^\prime (z)$ respectively. In this paper, we give simple proofs and improved version of various results proved in [1], concerning the zeros of a polynomial and its derivative.
Mir,M. Ibrahim, Wani,I. Ahmad and Nazir,I. (2022). On the zeros and critical points of a polynomial. Mathematical Analysis and its Contemporary Applications, 4(1), 25-28. doi: 10.30495/maca.2021.1938758.1028
MLA
Mir,M. Ibrahim, , Wani,I. Ahmad, and Nazir,I. . "On the zeros and critical points of a polynomial", Mathematical Analysis and its Contemporary Applications, 4, 1, 2022, 25-28. doi: 10.30495/maca.2021.1938758.1028
HARVARD
Mir M. Ibrahim, Wani I. Ahmad, Nazir I. (2022). 'On the zeros and critical points of a polynomial', Mathematical Analysis and its Contemporary Applications, 4(1), pp. 25-28. doi: 10.30495/maca.2021.1938758.1028
CHICAGO
M. Ibrahim Mir, I. Ahmad Wani and I. Nazir, "On the zeros and critical points of a polynomial," Mathematical Analysis and its Contemporary Applications, 4 1 (2022): 25-28, doi: 10.30495/maca.2021.1938758.1028
VANCOUVER
Mir M. Ibrahim, Wani I. Ahmad, Nazir I. On the zeros and critical points of a polynomial. MACA, 2022; 4(1): 25-28. doi: 10.30495/maca.2021.1938758.1028
