Cubic Equation calculator

📐 Cubic Equation Solver

Enter coefficients for ax³ + bx² + cx + d = 0

Coefficient a (x³)

Coefficient b (x²)

Coefficient c (x)

Constant d

x³ - 6x = 0

📊 Solutions

Roots and equation analysis

Root 1 (x₁) 0

Root 2 (x₂) 0

Root 3 (x₃) 0

Discriminant 0

📈 Function Graph

Cubic function visualization

🎯 3D Cubic Surface

Interactive 3D function visualization

Drag to rotate • Scroll to zoom

Understanding Cubic Equations

Cubic equations are polynomial equations of degree three. They have the general form ax³ + bx² + cx + d = 0 where a ≠ 0. These equations always have at least one real root and can have up to three real roots. The discriminant helps determine the nature of the roots.

Cardano's Formula

The analytical solution method for cubic equations, involving complex calculations with radicals and trigonometric functions.

Discriminant Analysis

Positive discriminant: 3 distinct real roots
Zero discriminant: Multiple roots
Negative discriminant: 1 real, 2 complex roots

Applications

Used in physics for motion equations, economics for optimization problems, and engineering for design calculations.

Advanced Cubic Equation Calculator