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
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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