# Definition:Quartic Equation

## Definition

A quartic equation is a polynomial equation of the form:

$a x^4 + b x^3 + c x^2 + d x + e = 0$

such that $a \ne 0$.

## Examples

### Example: $6 z^4 - 25 z^3 + 32 z^2 + 3 z - 10 = 0$

The quartic equation:

$6 z^4 - 25 z^3 + 32 z^2 + 3 z - 10 = 0$

has solutions:

$-\dfrac 1 2, \dfrac 2 3, 2 + i, 2 - 1$

## Also see

• Results about quartic equations can be found here.

## Historical Note

The solution of the quartic equation followed soon after the solution of the cubic.

It was included in Gerolamo Cardano's Artis Magnae, Sive de Regulis Algebraicis of $1545$, along with his solution of the cubic, which had been solved some few decades earlier by Scipione del Ferro.

It was solved by Lodovico Ferrari, who was a student of Cardano's.