Definition:Quintic Equation

Definition

Let $f(x) = a x^5 + b x^4 + c x^3 + d x^2 + e x + f$ be a polynomial function over a field $k$ of degree $5$.

Then the equation $f(x) = 0$ is the general quintic equation over $k$.

In general, it can not be solved analytically.

This fact is proved by the Abel-Ruffini Theorem.