Discriminant Calculator
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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Explore Allday Everyday Math →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.