A

David

Darling

fundamental theorem of algebra

The fundamental theorem of algebra is the result that every algebraic equation of the nth degree

 

    a0xn + a1xn-1 + ... + an-1x + an = 0

 

whose coefficients are real numbers possesses at least one real or complex root. An algebraic equation of the nth degree with one unknown, and real coefficients, possesses exactly n roots, provided every solution (real and complex) is counted according to its mutliplicity.