Discriminant Calculator

Discriminant (b²-4ac)
Number of Real Solutions
Solution Type

How It Works

This discriminant calculator uses established formulas to provide accurate results.

The basic rule:

  • Discriminant Δ = b² - 4ac
  • Δ > 0: two real solutions
  • Δ = 0: one repeated solution
  • Δ < 0: two complex solutions

Results are estimates. Consult a professional for critical decisions.

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Frequently Asked Questions

What is the discriminant?

The discriminant is the expression b² - 4ac from inside the square root of the quadratic formula. It determines whether the quadratic has 2 real, 1 real, or 0 real solutions without actually solving.

Why does a negative discriminant mean no real solutions?

A negative discriminant means you would need to take the square root of a negative number, which is not a real number. The solutions involve the imaginary unit i = √(-1).

Can I use the discriminant for a quick check?

Yes! Before solving a quadratic, compute the discriminant first. It tells you how many solutions to expect and whether factoring is even possible over the integers.