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