On a case of all pairs of polynomial zeros bad
Commun. Korean Math. Soc. 2003 Vol. 18, No. 4, 661-667
Printed December 1, 2003
Seon-Hong Kim
Chosun University
Abstract : In this paper, we show, for a positive integer $m$ and a large odd integer $n$, the polynomial equation $$ \prod_{k=0}^n (x-k^{1+\frac 1m})+\prod_{k=n+1}^{2n+1} (x- k^{1+\frac 1m})=0 $$ has a real zero on $$ \left( (n+1)^{1+\frac 1m}, \, \, (n+1)^{1+\frac 1m}+\frac 12\right) $$ and $$\left( (n+1)^{1+\frac 1m}+\frac 12, \, \,(n+2)^{1+\frac 1m}\right), $$ respectively.
Keywords : zero, polynomial, bad pair, good pair
MSC numbers : Primary 30C15; Secondary 26C10
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