Discriminant Calculator | Quadratic Equation Solver
Calculate the discriminant of a quadratic equation (ax² + bx + c = 0) and determine the nature of roots. Visualize the discriminant and copy results easily.
Understand the Discriminant (\(\Delta\))
The discriminant, denoted as \(\Delta\), of a quadratic equation , is given by the formula: . It helps determine the nature of the roots.
Discriminant Result:
Discriminant Value (\(\Delta\)):
Nature of Roots:
Discriminant Visualization
Understanding the Discriminant
The discriminant is a value calculated from the coefficients of a quadratic equation, \(ax^2 + bx + c = 0\), and is given by the formula \(\Delta = b^2 - 4ac\). It provides key information about the nature of the roots of the quadratic equation:
- If \(\Delta > 0\): The equation has two distinct real roots. This means the parabola intersects the x-axis at two different points.
- If \(\Delta = 0\): The equation has exactly one real root, which is a repeated root. The vertex of the parabola touches the x-axis.
- If \(\Delta < 0\): The equation has no real roots, but two complex conjugate roots. The parabola does not intersect the x-axis.
Understanding the discriminant helps in quickly determining the type of solutions a quadratic equation will have without explicitly solving for the roots. This tool visualizes these concepts, making it easier to grasp the relationship between the discriminant and the roots.
Source: Wikipedia - Discriminant