%0 Journal Article %T On the zeros and critical points of a polynomial %J Mathematical Analysis and its Contemporary Applications %I Research & Science Group Ltd %Z 2716-9898 %A Mir, Mohammad Ibrahim %A Wani, Irfan Ahmad %A Nazir, Ishfaq %D 2022 %\ 01/01/2022 %V 4 %N 1 %P 25-28 %! On the zeros and critical points of a polynomial %R 10.30495/maca.2021.1938758.1028 %X 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. %U https://www.macajournal.com/article_686557_580a51528933c5f12a9f2b13c74a0b56.pdf