Gauss Legacy Union oO煞氣a高斯的傳人Oo

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero.

Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.

The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n complex roots. The equivalence of the two statements can be proven through the use of successive polynomial division.

代數基本定理說明,任何一個一元複係數多項式方程都至少有一個複數根。也就是說,複數域是代數封閉的。約翰·卡爾·弗瑞德呂希·高斯推導。