Definition:Quartic Equation

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

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

Also see

 * Ferrari's Method: an algebraic technique for finding the roots of a general quartic.