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Quadratic Equation Solver

Solve ax² + bx + c = 0 with step-by-step solution and vertex form

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Quadratic Solver: ax² + bx + c = 0

Equation
x² - 5x + 6 = 0
Roots
Root 1 (x1)
3
Root 2 (x2)
2
Discriminant (b²-4ac)
1
Nature of Roots
Two real distinct roots
Vertex (h, k)
(2.5, -0.25)
Axis of Symmetry
x = 2.5
Sum of Roots
5
Product of Roots
6
Step-by-step Solution

The Quadratic Formula

For the equation ax² + bx + c = 0, the roots are given by: x = (-b ± sqrt(b² - 4ac)) / (2a)

The Discriminant

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

If D > 0: Two distinct real roots. If D = 0: One repeated real root. If D < 0: Two complex conjugate roots.