Discriminant Calculator
Compute b^2-4ac for a quadratic to determine if roots are real and distinct, repeated, or complex. Returns both the discriminant value and real root count.
How to use this tool
- Enter coefficient a, coefficient b and coefficient c in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your discriminant and the full breakdown beneath it.
Formula
D = b^2 - 4ac
How it works
Compute D = b² − 4ac. D > 0: two distinct real roots; D = 0: one repeated real root; D < 0: no real roots.
Worked example
x^2 + 3x + 2 = 0
- a=1, b=3, c=2
- D = 9 - 8 = 1 > 0
- Two distinct real roots.
Common mistakes to avoid
- Computing b^2 - 4ac as (b-4ac)^2 by misreading the order of operations; squaring must happen before subtraction.
- Using the coefficient of x (not x^2) as a, shifting all three coefficients by one position.
- Forgetting to check whether a is zero before interpreting the result; if a=0 the formula does not apply.
Key terms
Frequently asked questions
- Does a discriminant of zero mean there is no solution?
- No. D=0 means exactly one (repeated) real solution exists: x = -b/(2a). The parabola is tangent to the x-axis.
- How does the discriminant tell me the number of real roots?
- D > 0: two distinct real roots. D = 0: one repeated real root. D < 0: no real roots (complex conjugate pair).
- Can I use the discriminant for cubics or higher-degree polynomials?
- The formula D = b^2 - 4ac applies only to quadratics (degree 2). Higher-degree polynomials have their own discriminant formulas.