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