Quadratic Equation Calculator
Understanding Quadratic Equations: Complete Guide
What is a Quadratic Equation?
A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a ≠0. These equations are fundamental in algebra and appear in various scientific and engineering applications.
Quadratic Formula
The solutions are found using the quadratic formula:
x = [-b ± √(b² – 4ac)] / (2a)
Key Components
| Term | Description |
|---|---|
| Discriminant (D) | D = b² – 4ac determines root nature |
| Coefficient a | Determines parabola’s opening direction |
| Vertex | (-b/2a, -D/4a) – turning point of parabola |
Discriminant Cases
- D > 0: Two distinct real roots
- D = 0: Exactly one real root
- D < 0: Two complex conjugate roots
Real-World Applications
Projectile motion calculations
Optimization problems
Engineering design
Economic forecasting
FAQs
Can a quadratic equation have 3 solutions?
No, fundamental theorem of algebra guarantees exactly 2 solutions (real or complex).
What if a = 0?
The equation becomes linear (bx + c = 0), not quadratic.