• Sums of two polynomials with each having real zeros symmetric with the other

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/112/02/0283-0288

• # Keywords

Polynomial; zero; geometric progression

• # Abstract

Consider the polynomial equation$$\prod\limits_{i = 1}^n {(x - r_i )} + \prod\limits_{i = 1}^n {(x + r_i )} = 0,$$ where 0 &lt;r1 ⪯ {irt}2⪯... ⪯rn All zeros of this equation lie on the imaginary axis. In this paper, we show that no two of the zeros can be equal and the gaps between the zeros in the upper half-plane strictly increase as one proceeds upward. Also we give some examples of geometric progressions of the zeros in the upper half-plane in casesn = 6, 8, 10.

• # Author Affiliations

1. School of Mathematical Sciences, Seoul National University, Seoul - 151-742, Korea

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019