# ON SOME ROOT BEHAVIORS OF CERTAIN SUMS OF POLYNOMIALS

• Chong, Han-Kyol (Department of Mathematics Sookmyung Women's University) ;
• Kim, Seon-Hong (Department of Mathematics Sookmyung Women's University)
• Published : 2016.01.31
• 48 7

#### Abstract

It is known that no two of the roots of the polynomial equation (1) $$\prod\limits_{l=1}^{n}(x-r_l)+\prod\limits_{l=1}^{n}(x+r_l)=0$$, where 0 < $r_1{\leq}r_2{\leq}{\cdots}{\leq}r_n$, can be equal and all of its roots lie on the imaginary axis. In this paper we show that for 0 < h < $r_k$, the roots of $$(x-r_k+h)\prod\limits_{{l=1}\\{l{\neq}k}}^{n}(x-r_l)+(x+r_k-h)\prod\limits_{{l=1}\\{l{\neq}k}}^{n}(x+r_l)=0$$ and the roots of (1) in the upper half-plane lie alternatively on the imaginary axis.

#### Keywords

sums of polynomials;roots;root squeezing

#### Acknowledgement

Supported by : Sookmyung Women's University

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#### Cited by

1. Root and critical point behaviors of certain sums of polynomials vol.128, pp.2, 2018, https://doi.org/10.1007/s12044-018-0402-7