CentralNotice From Wikipedia, the free encyclopedia Jump to navigation Jump to search Every polynomial has a real or complex root Not to be confused with Fundamental theorem of arithmetic . The fundamental theorem of algebra also known as d'Alembert's theorem [1] or the d'Alembert-Gauss theorem [2] 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 b...