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arXiv · 2508.15818

Analysis of the Distribution and Asymptotic Approximations of Roots of the Polynomial Equation $$ z^{n+1}=(1+z)^n, n \in \mathbb{N} $$ in the Complex Plane

Hailu Bikila Yadeta
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Abstract

We study the spatial distribution of the positive, negative and non-real complex roots $z_n $ of the sequence the $(n+1)$th degree polynomial equation $$ z^{n+1}=(1+z)^n,\quad n \in \mathbb{N}.$$ We establish asymptotic approximations to the sequence of the negative, the positive and the non-real complex roots of the equation as $n\rightarrow \infty $. In addition, we discuses the possible areas of applications of the current problem.

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Hailu Bikila Yadeta. 2025-08-17. Analysis of the Distribution and Asymptotic Approximations of Roots of the Polynomial Equation $$ z^{n+1}=(1+z)^n, n \in \mathbb{N} $$ in the Complex Plane. https://arxiv.org/abs/2508.15818

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