Discriminant Calculator
ax² + bx + c = 0
Results
How to Use
- Enter the coefficients a, b, and c of your quadratic equation
- Make sure a is not zero (otherwise it's not a quadratic equation)
- Click "Calculate Discriminant" to find the discriminant
- View the analysis of the equation's roots
About the Discriminant
The discriminant (Δ) of a quadratic equation ax² + bx + c = 0 is given by:
Δ = b² - 4ac
The discriminant tells us about the nature of the roots:
- If Δ > 0: Two distinct real roots
- If Δ = 0: One repeated real root
- If Δ < 0: Two complex conjugate roots
The roots can be found using the quadratic formula:
x = (-b ± √Δ) / (2a)
Common Examples
| Equation | Discriminant | Roots |
|---|---|---|
| x² - 5x + 6 = 0 | 1 | 2 and 3 |
| x² - 2x + 1 = 0 | 0 | 1 (repeated) |
| x² + 1 = 0 | -4 | ±i |
| x² + 2x + 2 = 0 | -4 | -1 ± i |
Applications
- Solving quadratic equations
- Analyzing polynomial functions
- Physics and engineering calculations
- Mathematical modeling
- Optimization problems
Advertisement Space