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arXiv · 2304.03776

A short ODE proof of the Fundamental Theorem of Algebra

Ramona Anton·Nicolae Mihalache·François Vigneron
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Abstract

We propose a short proof of the Fundamental Theorem of Algebra based on the ODE that describes the Newton flow and the fact that the value $|P(z)|$ is a Lyapunov function. It clarifies an idea that goes back to Cauchy.

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Ramona Anton, Nicolae Mihalache, François Vigneron. 2023-04-06. A short ODE proof of the Fundamental Theorem of Algebra. https://arxiv.org/abs/2304.03776

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