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