📐 Quadratic Equation Solver
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📌 Understanding Quadratic Equations
A quadratic equation is a second-degree polynomial equation in a single variable x:
- ax² + bx + c = 0
- The solutions (roots) of the equation are found using the quadratic formula:
- x = (-b ± √(b² – 4ac)) / 2a
📌 Example Calculations
| a | b | c | Roots |
|---|---|---|---|
| 1 | -3 | 2 | x = 2, x = 1 |
| 1 | 2 | 1 | x = -1, x = -1 |
| 1 | 4 | 5 | No Real Roots |
🔧 Practical Applications of Quadratic Equations
1. Physics & Engineering: Used in projectile motion and mechanical systems.
2. Finance & Economics: Helps in modeling cost and revenue functions.
3. Computer Science: Essential in graphics, machine learning, and algorithms.
❓ FAQs
Q1: How do I solve a quadratic equation?
✅ Use the quadratic formula x = (-b ± √(b² – 4ac)) / 2a.
Q2: What happens if the discriminant is negative?
✅ If b² – 4ac is negative, the equation has no real roots.
Q3: Can quadratic equations have one solution?
✅ Yes, when the discriminant is zero, both roots are the same.
Q4: Where are quadratic equations commonly used?
✅ Quadratic equations are used in **physics, engineering, economics, and computer science**.
Q5: Why are quadratic equations important?
✅ They help in **solving problems related to motion, optimization, and natural sciences**.