Definition:Quintic Equation

Definition
Let $f \left({x}\right) = a x^5 + b x^4 + c x^3 + d x^2 + e x + f$ be a polynomial function over a field $\mathbb k$ of degree $5$.

Then the equation $f \left({x}\right) = 0$ is the general quintic equation over $\mathbb k$.

Also see

 * Abel-Ruffini Theorem, which proves that, in general, a quintic equation can not be solved analytically.


 * Definition:Quadratic Equation
 * Definition:Cubic Equation
 * Definition:Quartic Equation