MyAIUtility

Quadratic Equation Solver

Solve quadratic equations of the form ax² + bx + c = 0

ax² + bx + c = 0
x² +
x +
= 0
Equation: x² - 5x + 6 = 0

Solution

Two distinct real roots

Discriminant (b² - 4ac):

1

D > 0: Two distinct real roots

Roots:

x1 =3
x2 =2

Vertex

(2.5, -0.25)

Axis of Symmetry

x = 2.5

Y-Intercept

(0, 6)

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

The discriminant D = b² - 4ac determines the nature of the roots:

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

Example Equations