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Sums of two polynomials with each having real zeros symmetric with the other
- Authors
- Kim, SH (Kim, SH)
- Issue Date
- May-2002
- Publisher
- INDIAN ACADEMY SCIENCES
- Citation
- PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, v.112, no.2, pp 283 - 288
- Pages
- 6
- Journal Title
- PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
- Volume
- 112
- Number
- 2
- Start Page
- 283
- End Page
- 288
- ISSN
- 0253-4142
0973-7685
- Abstract
- Consider the polynomial equation [GRAPHICS] where 0 < r(1) LE; r(2) LE; ... LE; r(n) 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 cases n=6, 8, 10.
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