Gauss-Lucas theorem

proper noun

A theorem that gives a geometric relation between the roots of a polynomial P and the roots of its derivative P′. It states that the roots of P′ all lie within the convex hull of the roots of P.

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Meanings

proper nounthe Gauss-Lucas theorem
  1. complex analysisA theorem that gives a geometric relation between the roots of a polynomial P and the roots of its derivative P′. It states that the roots of P′ all lie within the convex hull of the roots of P.

Origin

Named after Carl Friedrich Gauss and Félix Lucas.

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Cite this entry
APA

Gauss-Lucas theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Gauss-Lucas%20theorem

MLA

“Gauss-Lucas theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Gauss-Lucas%20theorem. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Gauss-Lucas theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Gauss-Lucas%20theorem.

Source: Gauss-Lucas theorem on Wiktionary, CC BY-SA 4.0.