A quintic function in algebra is a function of the form

\[h(x)=a x^{5}+b x^{4}+c x^{3}+d x^{2}+e x+f\]

where \(a\), \(b\), \(c\), \(d\), \(e\) and \(f\) are members of rational numbers field, real numbers field or complex numbers field, and \(a \neq 0\). That is, a quintic function is a polynomial of degree five.

Putting \(h(x)=0\) and assuming \(a \neq 0\) we get a quintic equation of the form : \[a x^{5}+b x^{4}+c x^{3}+d x^{2}+e x+f=0\]