FundamentalTheoremOfAlgebra

Fundamental theorem of algebra (English)

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If p(z) is a polynomial function,

p(z)=a₀+a₁z+a₂z²+...+a_N−1z^N−1+z^N

with complex coefficients a₀, a₁... then there is some complex number w for which p(w)=0.

Every non-constant polynomial has at least one root in C; more generally, for a monic polynomial p of order n we may write

p(z) =

n
∏
i=1

(z−z_i)

where z_i ∈ C are the roots of p .

broader:: (en) Algebra; (en) Theorem
references:: (en) Complex number; (en) Polynomial function; (en) Root of an equation
referenced:: (en) Argand