Solving Quadratic Equations By The Quadratic Formula Worksheet Page 16
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16The Discriminant!
The quantity under the radical in the quadratic formula
can tell us alot about the nature of the solutions.
Therefore, it is given a special name. The
discriminant
is
b
2
- 4ac
If the discriminant is less than zero, then you will be
taking the square root of a negative number yielding
complex solutions.
If the discriminant equals zero, you have one real
solution (namely -b/2a)
If the discriminant is greater than zero, then we have two
different real solutions. This is summarized in the
following chart:
discriminant Types of solutions
2
b
- 4ac < 0 Two complex conjugates
2
b
-4ac = 0 One real (double root)
2
b
- 4ac > 0 Two different real roots
16
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