1
MA 15200
Lesson 15
Section 1.5 (part 2)
I
The Discriminant
The part of the quadratic formula under the radical sign
2
(
4
)
b
ac

is called the
discriminant.
(Some textbooks call it the determinant.)
Note:
The discriminant is
without the radical sign.
1.
If
2
4
0
b
ac

=
, then the formula would be
0
2
2
b
b
x
a
a
 ±
=
= 
.
There will only
be
one rational solution.
2.
If
2
4
b
ac

equals a positive perfect square number, then the formula would be
2
2
2
b
k
b
k
x
a
a
 ±
 ±
=
=
, where
k
is a positive rational number.
There will be
two
rational solutions.
3.
If
2
4
b
ac

equals a positive nonperfect square number, then the formula would
be
2
b
n
x
a
 ±
=
, where
n
is a nonperfect square number.
There will be
two
conjugate irrational solutions
because the solutions include a radical.
4.
If
2
4
b
ac

equals a negative number, then the formula will be
2
2
2
b
n
b
n
x
i
a
a
a
 ± 

=
=
±
, where
n
is a positive number.
There will be
two
conjugate complex solutions.
Ex 1:
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 Fall '09
 Determinant, Quadratic Formula, Irrational number, nonperfect square number

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