V.K.Jain:Generalization of a result on the roots of a trinomial equation, p.143-147

Abstract:

It is known that the trinomial equation

$$cz^n-z+1=0,$$

has a root, in both the regions $\vert z-1\vert\geq 1$, $\vert z-1\vert\leq 1$, $(n\geq 2)$, as well as the exterior of every circle, which passes through the origin, $(n\geq 3)$. We have obtained a generalization, as well as an extension of this result and have shown that the polinomial

$$cz^n-(z-1)^m, c\not=0,$$

has a zero, in both the regions $\vert z-1\vert\geq 1$, $\vert z-1\vert\leq 1$, $(1\leq m\leq n-1)$, as well as, in the exterior of every circle, which passes through the origin, $(1\leq m\leq n-2)$

Key Words: Zeros of complex polinomials

2000 Mathematics Subject Classification: Primary: 12D10,
Secondary: 30C15.

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