Cubic Equation Calculator
ax³ + bx² + cx + d = 0
Results
How to Use
- Enter the coefficients a, b, c, and d of your cubic equation
- Make sure a is not zero (otherwise it's not a cubic equation)
- Click "Solve Equation" to find all roots
- View the results and step-by-step solution
About Cubic Equations
A cubic equation has the form:
ax³ + bx² + cx + d = 0
Properties:
- Every cubic equation has exactly three roots (real or complex)
- If all coefficients are real, then either:
- All three roots are real
- One root is real and two are complex conjugates
- The sum of the roots is -b/a
- The product of the roots is -d/a
Common Examples
| Equation | Roots |
|---|---|
| x³ - 1 = 0 | 1, -0.5 ± 0.866i |
| x³ + x = 0 | 0, ±i |
| x³ - 6x² + 11x - 6 = 0 | 1, 2, 3 |
| x³ + x² + x + 1 = 0 | -1, ±i |
Applications
- Solving polynomial equations
- Finding intersection points of curves
- Optimization problems
- Physics and engineering calculations
- Computer graphics and 3D modeling
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