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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