# Definition:Quartic Equation

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*This page is about Quartic Equation. For other uses, see Quartic.*

## 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

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

- 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.

## Sources

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 9$: Solutions of Algebraic Equations: Quartic Equation - 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): Where to begin... - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**quartic equation**