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ON SOME ROOT BEHAVIORS OF CERTAIN SUMS OF POLYNOMIALSopen access

Authors
Chong, Han-KyolKim, Seon-Hong
Issue Date
Jan-2016
Publisher
KOREAN MATHEMATICAL SOC
Keywords
sums of polynomials; roots; root squeezing
Citation
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.53, no.1, pp.21 - 28
Journal Title
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
Volume
53
Number
1
Start Page
21
End Page
28
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/3595
DOI
10.4134/BKMS.2016.53.1.021
ISSN
1015-8634
Abstract
It is known that no two of the roots of the polynomial equation (1) Pi(n)(l=1) (x - r1) + Pi(n)(l=1) (x + r1) = 0, where 0 < r(1) <= r(2) <= ... <= 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) Pi(n)(l=1l not equal k) (x - r(1)) + (x + r(k) - h) Pi(n)(l=1l not equal k) (x + r(1)) = 0 and the roots of (1) in the upper half-plane lie alternatively on the imaginary axis.
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