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Quadratic Equation Solver
Solve quadratic equations of the form ax² + bx + c = 0
ax² + bx + c = 0
Standard quadratic equation form
How Quadratic Equations Work
Quadratic equations are second-degree polynomial equations that can be solved using the quadratic formula, which provides the roots based on the discriminant value.
Enter coefficients a, b, and c from your equation
Click "Solve Equation" to calculate the roots
View the nature of roots based on discriminant
See step-by-step solution process
Copy roots for use in other applications
Quadratic Formula:
x = [-b ± √(b² - 4ac)] / 2a
Discriminant (Δ) = b² - 4ac
Determines the nature of the roots
Roots Classification:
Δ > 0: Two distinct real roots
Δ = 0: One repeated real root
Δ < 0: Two complex conjugate roots
Common Examples:
x² - 5x + 6 = 0: Roots at x=2, x=3 (Δ=1)
x² - 4x + 4 = 0: Root at x=2 (Δ=0)
x² + 2x + 5 = 0: Complex roots (Δ=-16)
Real-World Applications:
Physics: Projectile motion and trajectories
Engineering: Structural analysis and optimization
Economics: Profit maximization and break-even analysis
Computer Graphics: Curve fitting and 3D modeling