Discriminant Calculator

Calculate b² - 4ac for quadratic equations

Coefficient a (x² term)

Coefficient b (x term)

Constant c

Formula

Δ = b² - 4ac

For ax² + bx + c = 0

Δ > 0

Two distinct real roots

Parabola crosses x-axis twice

Δ = 0

One repeated real root

Parabola touches x-axis once

Δ < 0

Two complex conjugate roots

Parabola doesn't touch x-axis

Algebra

• Determining root nature

• Solving quadratics

• Factorability check

Graphing

• X-intercepts prediction

• Parabola behavior

• Function analysis

Problem Solving

• Solution existence

• Optimization problems

• Physics applications

Perfect Square

Δ = 0 means equation is a perfect square trinomial

Integer Roots

Δ is a perfect square suggests rational roots

In Quadratic Formula

x = (-b ± √Δ) / (2a)