Seon-Hong Kim
Articles written in Proceedings – Mathematical Sciences
Volume 112 Issue 2 May 2002 pp 283-288
Sums of two polynomials with each having real zeros symmetric with the other
Consider the polynomial equation$$\prod\limits_{i = 1}^n {(x - r_i )} + \prod\limits_{i = 1}^n {(x + r_i )} = 0,$$ where 0 <
Volume 128 Issue 2 April 2018 Article ID 0023 Research Article
Root and critical point behaviors of certain sums of polynomials
SEON-HONG KIM SUNG YOON KIM TAE HYUNG KIM SANGHEON LEE
It is known that no two roots of the polynomial equation $$\prod^{n}_{j=1}(x-rj)+\prod^{n}_{j=1}(x+rj)=0$$,
where 0 < $r_{1}\leq r_{2}\leq \cdots\leq r_{n}$, can be equal and the gaps between the roots of (1) in the upper half-plane strictly increase as one proceeds upward, and for 0 < $h$ < $r_{k}$, the roots of $$(x-r_{k}-h)\prod^{n}_{{j=1}\atop{j\neq k}}(x-r_{j})+(x+r_{k}+h)\prod^{n}_{{j=1}\atop{j\neq k}}(x+r_{j})=0$$
and the roots of (1) in the upper half-plane lie alternatively on the imaginary axis. In this paper, we study how the roots and the critical points of (1) and (2) are located.
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