Cubic Equation Solver
Solve cubic equations of the form ax³ + bx² + cx + d = 0. Finds all real and complex roots.
Formula
ax³ + bx² + cx + d = 0 (solved using Cardano's formula)
- Converts to depressed cubic t³ + pt + q = 0
- Uses Cardano's formula for roots
- Discriminant > 0: three distinct real roots
- Discriminant = 0: repeated roots
- Discriminant < 0: one real root, two complex conjugates
Cubic Equation Example
Inputs
- a (coefficient of x³): 1
- b (coefficient of x²): 0
- c (coefficient of x): -1
- d (constant): 0
Solve x³ - x = 0. Factors as x(x² - 1) = x(x-1)(x+1), so roots are x = 0, 1, -1.
Frequently asked questions
What is a cubic equation?
A cubic equation is a polynomial of degree 3: ax³ + bx² + cx + d = 0 with a ≠ 0. It always has at least one real root.
How many roots can a cubic have?
A cubic can have 1, 2, or 3 real roots. Complex roots always appear in conjugate pairs.
What is Cardano's formula?
Cardano's formula is a method to solve cubic equations algebraically, converting them to a depressed form and using specific arithmetic.
What does the discriminant mean?
Discriminant > 0: 3 distinct real roots; = 0: repeated roots; < 0: 1 real root + 2 complex conjugates.