Editing Zero of a function (section)

== Polynomial roots ==
{{main|Properties of polynomial roots}}
Every real polynomial of odd [[Degree of a polynomial|degree]] has an odd number of real roots (counting [[Multiplicity (mathematics)#Multiplicity of a root of a polynomial|multiplicities]]); likewise, a real polynomial of even degree must have an even number of real roots. Consequently, real odd polynomials must have at least one real root (because the smallest odd whole number is 1), whereas even polynomials may have none. This principle can be proven by reference to the [[intermediate value theorem]]: since polynomial functions are [[Continuous function|continuous]], the function value must cross zero, in the process of changing from negative to positive or vice versa (which always happens for odd functions).

===Fundamental theorem of algebra===
{{main|Fundamental theorem of algebra}}
The fundamental theorem of algebra states that every polynomial of degree <math>n</math> has <math>n</math> complex roots, counted with their multiplicities. The non-real roots of polynomials with real coefficients come in [[complex conjugate|conjugate]] pairs.<ref name="Foerster" /> [[Vieta's formulas]] relate the coefficients of a polynomial to sums and products of its roots.