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Key Features
Instant Calculation
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The discriminant is a single number, b² − 4ac, that instantly reveals how many real roots a quadratic has — without needing to solve the whole equation first. This calculator finds a quadratic's discriminant and classifies its roots, with a full step-by-step solution.
How it works
Enter the quadratic's coefficients a, b, and c. The calculator applies the discriminant formula, b² − 4ac, and classifies the result: positive means two distinct real roots, zero means one repeated real root, and negative means two complex conjugate roots.
- Enter a (coefficient of x²).
- Enter b (coefficient of x).
- Enter c (constant).
- Click Calculate to see your results.
Examples
x² − 3x + 2 = 0
The discriminant is 1, which is positive — so this quadratic has two distinct real roots (in fact, x = 1 and x = 2).
Who should use it
- Quickly checking whether a quadratic has real solutions before attempting to solve it.
- Verifying discriminant calculations for an algebra homework problem.
Industry applications
- Algebra education
- Engineering and physics problems involving quadratic equations
Advantages
- Classifies the root type instantly without solving the full quadratic formula.
- Uses the exact discriminant formula, not an approximation.
Limitations
- Only classifies the roots — use a dedicated quadratic solver to find their exact values.
Common mistakes to avoid
- Forgetting the negative sign in −4ac, which flips the result's sign and classification.
- Assuming a negative discriminant means "no solution" — it means no REAL solution; there are still two complex roots.
Best practices
- Use the discriminant as a quick check before fully solving a quadratic, especially when you only need to know the root type, not the exact values.
Tips
- A discriminant of exactly zero means the parabola touches the x-axis at exactly one point — its vertex sits directly on the x-axis.