The **discriminant** of a quadratic
equation in the form is caluculated by
using the expression . Note that the
discriminant is found underneath the radical in the quadratic
formula.

The discriminant is useful because it reveals the number and nature of solutions to a quadratic equation:

If the value of the discriminant is **positive**, the
quadratic equation has **two real
solutions**.

If the value of the discriminant is **zero**, the quadratic
equation has **one real solution**.

If the value of the discriminant is **negative**, the
quadratic equation has **no real
solutions**. Rather, solutions
with an imaginary component are present.

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