Quadratic Equation Solver

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Roots, discriminant and vertex of ax² + bx + c = 0, with the complex pair where there are no real roots

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The coefficients

ax² + bx + c = 0 — set a to zero and it becomes a linear equation

a (x² term)

b (x term)

c (constant)

1x² − 5x + 6 = 0

Solution

x₁

x₂

Discriminant (b² − 4ac): 1
Which means: two distinct real roots
Vertex: (2.5000, -0.2500)

The discriminant tells you the shape of the answer before you find it: positive means two distinct roots, zero means a repeated one, negative means none that are real. Exam questions often ask only for that much.

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