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arXiv · 1803.04358

Quantitative Fundamental Theorem of Algebra

Daniel Perrucci·Marie-Françoise Roy
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Abstract

Using subresultants, we modify a recent real-algebraic proof due to Eisermann of the Fundamental Theorem of Algebra ([FTA]) to obtain the following quantitative information: in order to prove the [FTA] for polynomials of degree $d$, the Intermediate Value Theorem ([IVT]) is requested to hold for real polynomials of degree at most $d^2$. We also explain that the classical proof due to Laplace requires [IVT] for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.

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Daniel Perrucci, Marie-Françoise Roy. 2018-03-12. Quantitative Fundamental Theorem of Algebra. https://arxiv.org/abs/1803.04358

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