Degree 2 Polynomial with Zeros Calculator
Introduction & Importance
Degree 2 polynomials are fundamental in algebra, with real-world applications in physics, engineering, and economics. Calculating their zeros is crucial for solving equations and understanding the behavior of functions.
How to Use This Calculator
- Enter the coefficients a, b, and c of your degree 2 polynomial (ax² + bx + c).
- Click ‘Calculate’.
- View the results and chart below.
Formula & Methodology
The zeros of a degree 2 polynomial can be found using the quadratic formula:
x = [-b ± √(b² – 4ac)] / (2a)
Real-World Examples
Example 1: Physics – Projectile Motion
Given h = 64, v = 16, and g = 9.81, find the time it takes for the projectile to hit the ground.
t = v / g ± √(v² / g² – 4h / g)
Example 2: Economics – Supply and Demand
Given P = 10, Qd = 20, and Qs = 30, find the equilibrium price.
P = (Qd + Qs) / (1 / Pd + 1 / Ps)
Example 3: Engineering – Beam Deflection
Given L = 10, E = 200, I = 1, and w = 5, find the maximum deflection of a simply supported beam.
δ = 5wL⁴ / (384EI)
Data & Statistics
| Polynomial | Zero 1 | Zero 2 |
|---|---|---|
| x² + 5x + 6 | 2 | -3 |
| x² – 3x + 2 | 1 | 2 |
| Polynomial | Discriminant | Nature of Zeros |
|---|---|---|
| x² + 5x + 6 | 1 | Real and distinct |
| x² – 3x + 2 | 5 | Real and equal |
Expert Tips
- Always check the discriminant (b² – 4ac) to determine the nature of the zeros.
- For real-world applications, consider the physical meaning of the zeros.
- Use the calculator to verify your manual calculations.
Interactive FAQ
What is the discriminant?
The discriminant (b² – 4ac) determines the nature of the zeros of a quadratic equation.
What are the limitations of this calculator?
This calculator only works for real numbers. For complex zeros, use a different tool.