Quadratic Discriminant Calculator
Discriminant and root type for ax²+bx+c.
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ⓘ Live results
Results
- Discriminant
- 1
- Root nature
- Two distinct real roots
- a, b, c
- 1, -3, 2
Quick answer
The discriminant b^2-4ac tells you the nature of the roots: positive gives two real roots, zero gives one repeated root, negative gives complex roots.
D = b^2 - 4ac
How to use the Quadratic Discriminant Calculator
- 1Enter the quadratic coefficients a, b and c.
- 2Compute D = b^2 - 4ac.
- 3The sign of D tells you what kind of roots the equation has.
Worked example
Using the values the calculator loads with:
Inputs
- a1
- b-3
- c2
Results
- Discriminant1
- Root natureTwo distinct real roots
- a, b, c1, -3, 2
Frequently asked questions
What if D is negative?
The equation has no real solutions; the roots are complex numbers.
What if a = 0?
It's not a quadratic — use the linear equation solution instead.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.