📈 Cubic Equation Solver
Example equation: **2x³ – 4x² – 22x + 24 = 0** → Enter **a=2, b=-4, c=-22, d=24**
Result will appear here…
📌 What is a Cubic Equation?
A cubic equation is a polynomial equation of degree 3. It has the general form:
ax³ + bx² + cx + d = 0, where a ≠ 0.
It can have up to **three real roots** or a combination of real and complex roots.
📌 Applications of Cubic Equations
- Physics: Used in motion and energy calculations.
- Engineering: Essential in mechanical and civil engineering designs.
- Economics: Helps model profit functions and market trends.
- Data Science: Applied in machine learning and statistical models.
- Structural Analysis: Used in designing bridges and skyscrapers.
📌 Example Calculations
| Equation | Solution |
|---|---|
| 2x³ – 4x² – 22x + 24 = 0 | ✅ Roots: x = 4, x = -3, x = 1 |
| x³ – 6x² + 11x – 6 = 0 | ✅ Roots: x = 1, x = 2, x = 3 |
❓ FAQs
Q1: How many real roots can a cubic equation have?
✅ A cubic equation can have **one, two, or three real roots**.
Q2: Can cubic equations have complex solutions?
✅ Yes! If a cubic equation has only one real root, the other two are complex conjugates.
Q3: What happens if a = 0?
✅ If **a = 0**, the equation becomes quadratic, and the cubic solver won’t work.
Q4: What is the discriminant in a cubic equation?
✅ The discriminant determines the number of real and complex roots.
Q5: Where are cubic equations used?
✅ They are used in engineering, physics, and economics.