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arXiv · 1304.4261

A short proof of d'Alemberts theorem

Tord Sjödin
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Abstract

A classical theorem of d'Alembert states that if a polynomial P(x) with real coefficients has a non-real root x=a+ib, then it also has a root x=a-ib. We give a short and elementary inductive proof that avoids any properties of the complex conjugation operator.

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Tord Sjödin. 2013-04-10. A short proof of d'Alemberts theorem. https://arxiv.org/abs/1304.4261

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