Roots of polynomials and tangents of circles

Andrey Ryabichev; Konstantin Shcherbakov

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arXiv · 2401.12394

Roots of polynomials and tangents of circles

Andrey Ryabichev·Konstantin Shcherbakov

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Abstract

Given a real cubic function $f(x)$ with three roots, take an equilateral triangle $ABC$, the projections of which vertices are the roots of $f(x)$. There is a folklore fact that the vertical lines through the extrema of $f(x)$ are tangent to the inscribed circle of $ABC$. We generalise this fact to a regular $n$-gon and the corresponding degree $n$ polynomial.

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BibTeX RIS

Andrey Ryabichev, Konstantin Shcherbakov. 2024-01-22. Roots of polynomials and tangents of circles. https://arxiv.org/abs/2401.12394

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