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- W2334762605 abstract "It is known that no two of the roots of the polynomial equation (1) <TEX>$$prodlimits_{l=1}^{n}(x-r_l)+prodlimits_{l=1}^{n}(x+r_l)=0$$</TEX>, where 0 < <TEX>$r_1{leq}r_2{leq}{cdots}{leq}r_n$</TEX>, can be equal and all of its roots lie on the imaginary axis. In this paper we show that for 0 < h < <TEX>$r_k$</TEX>, the roots of <TEX>$$(x-r_k+h)prodlimits_{{l=1}{l{neq}k}}^{n}(x-r_l)+(x+r_k-h)prodlimits_{{l=1}{l{neq}k}}^{n}(x+r_l)=0$$</TEX> and the roots of (1) in the upper half-plane lie alternatively on the imaginary axis." @default.
- W2334762605 created "2016-06-24" @default.
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- W2334762605 date "2016-01-31" @default.
- W2334762605 modified "2023-09-26" @default.
- W2334762605 title "ON SOME ROOT BEHAVIORS OF CERTAIN SUMS OF POLYNOMIALS" @default.
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- W2334762605 doi "https://doi.org/10.4134/bkms.2016.53.1.021" @default.
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