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The roots of the quadratic equation
are given by the formula
The number
is called the discriminant of the equation. If , there are two different real roots, if there is a single real root, and if there are no real roots (but two different complex roots).
Let's work a few examples.
First, consider . Here , , and . Substituting in the formula gives us
So we have two solutions (depending on whether we take the sign or ):
and
.
Now we will solve . Here , , and , so
and the solutions are
and
.
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