📐 Cubic Equation Calculator
Solve cubic equations
ax³ + bx² + cx + d = 0
How to Use This Calculator
1
Enter Coefficients
Type a, b, c, d for equation ax³ + bx² + cx + d = 0
2
Solve
Get all three roots (real and/or complex)
Cardano's Method
For cubic equation: ax³ + bx² + cx + d = 0
- Normalize: x³ + Ax² + Bx + C = 0
- Depressed cubic: y = x + A/3
- Calculate Δ = (q²/4) + (p³/27)
- If Δ > 0: 1 real, 2 complex roots
- If Δ = 0: 2 or 3 real roots (some repeated)
- If Δ < 0: 3 distinct real roots
About Cubic Equation Calculator
The Cubic Equation Calculator solves cubic equations using Cardano's method, which systematically finds all three roots. A cubic equation always has three roots (counting complex roots and multiplicities).
Root Patterns
- Discriminant > 0: One real root and two complex conjugate roots
- Discriminant = 0: One, two, or three real roots (some may be repeated)
- Discriminant < 0: Three distinct real roots
Applications
- Algebra: Finding zeros of cubic polynomials
- Physics: Solving cubic equations in mechanics
- Engineering: Signal processing, control systems
Frequently Asked Questions
How many roots does a cubic equation have?
Every cubic equation has exactly three roots (counting complex roots and multiplicities).
What is Cardano's method?
Cardano's method converts the cubic to a depressed form, making it easier to solve using radicals.
Can every cubic equation be solved?
Yes! Unlike quartics, every cubic equation can be solved exactly using radicals (Cardano's formula).