Quadratic Equation Solver

Solve ax² + bx + c = 0 — roots, vertex, discriminant.

Result

x₁3
x₂2
Discriminant (b²−4ac)1
Vertex(2.5, -0.25)

Quadratic Equation Solver — FAQs

Quadratic formula?

x = (−b ± √(b²−4ac)) / 2a. Discriminant >0 → two real roots; =0 → one repeated root; <0 → complex pair.

What is the discriminant?

b²−4ac — positive gives two real roots, zero gives one, negative gives complex roots.

Can a quadratic have no real solutions?

Yes — negative discriminant means complex roots, e.g. x²+1=0 gives x=±i.

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