Definition:Quartic Equation

From ProofWiki
Jump to navigation Jump to search

Definition

A quartic equation is a polynomial equation of the form:

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


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.


Sources