Cubic Equation Calculator
Solve any third-order polynomial equation instantly. This calculator provides all three roots, including imaginary numbers if applicable.
General Form:
ax³ + bx² + cx + d = 0
Uses Cardano's Method and the Discriminant (Δ) to identify root types.
For x³ - 6x² + 11x - 6 = 0: Roots are x₁=1, x₂=2, x₃=3.
What is a cubic equation?
A cubic equation is a third-degree polynomial equation of the form ax³ + bx² + cx + d = 0, where a ≠ 0. It must have at least one real root.
How many roots does a cubic equation have?
Every cubic equation has exactly three roots (some may be identical or complex), according to the Fundamental Theorem of Algebra.
What is Cardano's formula?
Cardano's formula is a method for finding the roots of a cubic equation. It involves transforming the general cubic into a "depressed cubic" and using square and cube roots to find the solutions.
Can a cubic equation have complex roots?
Yes. A cubic equation can have one real root and two complex conjugate roots, or three real roots.
🔗 Related Calculators
📐 Formula
General Form:
ax³ + bx² + cx + d = 0
Uses Cardano's Method and the Discriminant (Δ) to identify root types.
📝 Example Calculation
For x³ - 6x² + 11x - 6 = 0: Roots are x₁=1, x₂=2, x₃=3.
❓ Frequently Asked Questions
What is a cubic equation?▼
A cubic equation is a third-degree polynomial equation of the form ax³ + bx² + cx + d = 0, where a ≠ 0. It must have at least one real root.
How many roots does a cubic equation have?▼
Every cubic equation has exactly three roots (some may be identical or complex), according to the Fundamental Theorem of Algebra.
What is Cardano's formula?▼
Cardano's formula is a method for finding the roots of a cubic equation. It involves transforming the general cubic into a "depressed cubic" and using square and cube roots to find the solutions.
Can a cubic equation have complex roots?▼
Yes. A cubic equation can have one real root and two complex conjugate roots, or three real roots.