Quadratic Functions Worksheet - Chapter 2 Page 6
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1102Chapter02_014_024.qxd
3/9/04
9:31 am
Page 19
Quadratic functions
Example
11
x
2
x
Solve the equation 2
8
7
0.
2
2x
8x
7
0
x
2
The coefficient of
2.
7
2
x
4x
0
So divide by 2.
2
7
2
x
7
4x
Subtract
from both sides.
2
2
7
2
2
(x
2)
(2)
x
2
x
Complete the square for
4
.
2
7
2
(x
2)
4
2
Add (2)
to both sides.
2
1
2
(x
2)
Combine the RHS.
2
1
x
2
Square root both sides.
2
Add 2 to both sides.
1
x
2
2
So the roots are either
1
x
2
2
1
or x
2
2
2
Note: Sometimes b
4ac is negative, and there are then no real solutions.
Exercise
2D
Solve these quadratic equations by completing the square (remember to leave your answer in
surd form):
x
2
x
x
2
x
6
1
0
12
3
0
1
2
2
2
x
10
x
5
x
4
x
2
0
3
4
x
2
x
x
2
x
3
5
0
2
7
4
5
6
x
2
x
x
x
2
4
8
10
3
7
8
x
x
2
10
x
2
x
9
15
6
2
0
5
8
2
0
19
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