Cubic Equation Calculator
Solve cubic equations and find all real and complex roots.
Enter Coefficients
ax³ + bx² + cx + d = 0
Equation
1x³ -6x² + 11x -6 = 0
Roots
Real Roots
x₍1₎ = 1
x₍2₎ = 2
x₍3₎ = 3
Discriminant Analysis
-0.0370
< 0: Three distinct real roots
About Cubic Equations
Cardano's Formula
Cubic equations are solved using Cardano's formula, which first converts the equation to a depressed cubic (without the x² term), then applies a substitution to find the roots.
Nature of Roots
- • A cubic equation always has at least one real root
- • It can have 3 real roots or 1 real + 2 complex conjugate roots
- • The discriminant determines the nature of roots