🔢 Quartic Equation Calculator

What is a Quartic Equation?

A polynomial equation of degree 4, in the form ax⁴+bx³+cx²+dx+e=0 (a≠0). It has at most 4 real roots; including complex numbers, it always has exactly 4 roots.

Solution Method

Uses Ferrari's formula or the Durand-Kerner numerical method. This calculator uses the Durand-Kerner iteration.

Types of Roots

4 real roots: graph crosses x-axis 4 times

2 real + 2 complex: graph crosses x-axis twice

4 complex roots: no x-axis crossings

Double root: graph is tangent to x-axis

Vieta's Formulas