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