Discriminant Calculator
Calculate the discriminant of quadratic equations and analyze the nature of roots
📐 Discriminant Calculator
x² - 5x + 6 = 0
Formula
Δ = b² - 4ac
Where:
- Δ =Discriminant (delta)
- a, b, c =Coefficients of ax² + bx + c = 0
- Δ > 0 =Two distinct real roots
- Δ = 0 =One repeated real root
- Δ < 0 =Two complex conjugate roots
About Discriminant
The discriminant (Δ = b² - 4ac) determines the nature and number of roots in a quadratic equation ax² + bx + c = 0.
Cases:
- • Δ > 0: Two distinct real roots
- • Δ = 0: One repeated real root (perfect square)
- • Δ < 0: Two complex conjugate roots
Quadratic Formula:
x = (-b ± √Δ) / (2a)
Applications:
- • Determining solvability of quadratic equations
- • Physics: projectile motion analysis
- • Engineering: optimization problems
- • Finance: break-even analysis
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.