# fundamental theorem of algebra

The fundamental theorem of algebra is the result that every algebraic equation of the *n*th degree

*a*_{0}*x ^{n}* +

*a*

_{1}

*x*

^{n-1}+ ... +

*a*

_{n-1}

*x*+

*a*= 0

_{n}

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