Dissemination of zeros of generalized derivative of a polynomial via matrix approach

• Date: 2025
• Main Authors: Mohammad, Ruqia, Purohit, Mridula, Liman, Abdul
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2025
• Subjects: matrix; eigen vaues; polynomial; zero; polar derivative; 30C10; 26D07
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2297
• Journal Title: Algebra and Discrete Mathematics

A polynomial of degree \(n\) is denoted by \(p(z):=\sum\limits_{j=0}^{n} a_{j}z^{j}\). Then, by classical Cauchy's result, $$|z|\le 1+ \max\bigg(\left|\frac {a_{n-1}}{a_{n}}\right|, \left|\frac {a_{n-2}}{a_{n}}\right|, \left|\frac {a_{n-3}}{a_{n}}\right|,...,\left|\frac {a_{0}}{a_{n}}\right|\bi...