Additional Mathematics Module 3 - Quadratic Equations Worksheets With Answer Key Page 25
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
332
2.4 SOLVING PROBLEMS INVOLVING (.b
- 4ac )
2
The discriminant b
- 4ac of the quadratic equation can be used to
a) find an unknown value in an equation
Example 1
Example 2
2
2
2
The quadratic equation x
- 2px + 25 = 0
The quadratic equation x
– 2kx = -(k – 1)
Has two equal roots. Find the value p
Has no roots. Find the range of values of k
2
2
2
x
- 2px + 25 = 0
x
– 2kx = -(k – 2)
2
2
Thus, a = 1, b = -2p , c = 25
x
– 2kx + (k – 2)
= 0
2
2
Using .b
- 4ac = 0
Compare with ax
+ bx + c = 0
2
2
(-2p)
– 4(1)(25) = 0
Thus .a = 1, b = - 2k , c = (k – 2)
2
2
4p
- 100 = 0
Using b
- 4ac < 0
2
2
2
4p
= 100
(-2k)
– 4(k
-2k + 1)< 0
2
2
2
p
= 25
4k
- 4k
+ 8k – 4 < 0
8k – 4 < 0
p =
25
8k < 4
p =
5
.k < 4
2.4.1
Find the values of m for each of the following quadratic equations which
has two equal roots
Exercises 4
2
2
1.
mx
- 4x + 1 = 0
2. x
– 6x + m = 0
2
2
3. x
– 2mx + 2m + 3 = 0
4. x
- 2mx - 4x + 1 = 0
24
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education