Discriminant Calculator

Unlock the nature of quadratic equation roots with our discriminant calculator. Enter coefficients and visualize the result.

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.

Coefficient of \({x ^ 2}\) (a):

Coefficient of \({x}\) (b):

Constant term (c):

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