6.5 the quadratic formula and the discriminant. we have a number of different way of finding the...
TRANSCRIPT
We have a number of different way of finding the roots if a quadratic
equations
#1. Making a table
#2. Factoring
#3. Completing the Square
Now a new way that comes from completing the square.
The Quadratic Formula
The Quadratic Formula
Solve for x by completing the square.
222
2
2
2
22
0
a
b
a
c
a
bxa
bx
a
cxa
bx
cbxax
cbxax
The Quadratic Formula
Solve for x by completing the square.
222
2
2
2
22
0
a
b
a
c
a
bxa
bx
a
cxa
bx
cbxax
cbxax
2
22
2
2
2
22
4
4
2
4
4
4
a
acb
a
bx
a
acb
a
bxa
bx
The Quadratic Formula
Solve for x by completing the square.
2
22
2
2
2
22
4
4
2
4
4
4
a
acb
a
bx
a
acb
a
bxa
bx
a
acbbx
a
acb
a
bx
a
acb
a
bx
2
4
2
4
2
4
4
2
2
2
2
2
Yes, you can remember this formula
Pop goes the Weaselhttp://www.youtube.com/watch?v=2lbABbfU6Zc&feature=related
Gilligan’s Islandhttp://www.youtube.com/watch?v=3CWTt9QFioY&feature=related
This one I can’t explainhttp://www.youtube.com/watch?v=haq6kpWdEMs&feature=related
How does it work
Equation:
1
5
3
0153 2
c
b
a
xx
6
13
6
5
6
135
6
12255
32
13455 2
x
x
x
a
acbbx
2
42
The Discriminant
The number in the square root of the quadratic formula.
acb 42
12425
6145
0652
2
xxGiven
The Discriminant
The Discriminant can be negative, positive or zero
If the Discriminant is positive,
there are 2 real answers.
If the square root is not a prefect square
( for example ),
then there will be 2 irrational roots
( for example ).
25
52
The Discriminant
The Discriminant can be negative, positive or zero
If the Discriminant is positive,
there are 2 real answers.
If the Discriminant is zero,there is 1 real answer.
If the Discriminant is negative,there are 2 complex answers.
complex answer have i.
Solve using the Quadratic formula
32
6
2
148
112
22
2
1482
148
2
1968
12
331488
0338
338
2
2
2
x
x
x
x
xx
xx
Solve using the Quadratic formula
ix
ii
x
x
x
xx
xx
23
2
4
2
6
2
46
2
166
2
52366
12
131466
0136
613
2
2
2
Describe the roots
Tell me the Discriminant and the type of roots
0, One rational root
0962 xx
0532 xx
Describe the roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots
0962 xx
0532 xx
Describe the roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots
0962 xx
0532 xx
0482 xx
Describe the roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots
80, Two irrational roots
0962 xx
0532 xx
0482 xx