Quadratic Equation Solver

Solve ax² + bx + c = 0 using the quadratic formula

1x² +-5x +6 = 0

Enter Coefficients

a (coefficient of x²)

b (coefficient of x)

c (constant term)

Solution

Discriminant (b² - 4ac)

1.0000

Two distinct real roots

Roots

x₁ = 3

x₂ = 2

Quadratic Formula:

x = (-b ± √(b² - 4ac)) / 2a

x = (-(-5) ± √(1.00)) / (2 × 1)

Vertex

(2.5000, -0.2500)

Axis of Symmetry

x = 2.5000

Y-Intercept

(0, 6)

Direction

opens upward

Understanding the Discriminant

D > 0: Two distinct real roots
D = 0: One repeated real root (double root)
D < 0: Two complex conjugate roots