Discriminant Calculator
Calculate b^2 - 4ac and determine the nature of the roots.
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Request a ToolHow to Use the Discriminant Calculator
This tool computes the discriminant of a quadratic equation and shows the roots.
- Enter coefficients. Provide a (non-zero), b, and c for the equation ax^2 + bx + c = 0.
- View the discriminant. The value of b^2 - 4ac and the nature of the roots appear instantly.
- See the roots. Both roots are displayed, including complex roots when the discriminant is negative.
About the Discriminant
The discriminant of a quadratic equation ax^2 + bx + c = 0 is the expression b^2 - 4ac. It determines the nature of the roots: if positive, the equation has two distinct real roots; if zero, one repeated real root; if negative, two complex conjugate roots. The discriminant is a quick way to classify quadratic equations without fully solving them.
Frequently Asked Questions
What does a positive discriminant mean?
A positive discriminant means the quadratic has two distinct real roots. The parabola crosses the x-axis at two points.
What does a zero discriminant mean?
A zero discriminant means the quadratic has exactly one repeated real root. The parabola touches the x-axis at one point (the vertex).
What does a negative discriminant mean?
A negative discriminant means there are no real roots. Instead, the equation has two complex conjugate roots, and the parabola does not cross the x-axis.