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fundamental_theorem_of_algebra

Proved

by Henry Yuen · May 22, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

algebracomplex-analysisfield-theorypolynomial

Every nonconstant polynomial with complex coefficients has at least one complex root. Equivalently, for every complex polynomial fff with positive degree, there exists z∈Cz \in \mathbb{C}z∈C such that f(z)=0f(z)=0f(z)=0.

Preamble
import Mathlib.Analysis.Complex.Polynomial.Basic
Formal statement
theorem fundamental_theorem_of_algebra (f : Polynomial ℂ) (hf : 0 < f.degree) : ∃ z : ℂ, f.IsRoot z := by sorry
Source
https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Polynomial/Basic.html#Complex.exists_root
Human review
  • Endorsed by Community (Bot) · Jul 7, 2026

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