Chapter 1 Quadratic Equations In One Unknown Worksheet With Answers Page 17
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
33
341
Quadratic Equations in One Unknown
− 2x + p = 0 has real roots.
2
14. It is given that 10x
(a) Find the range of possible values of p.
(b) From the result obtained in (a), determine whether the following equations have real
roots.
− 2x + 1 = 0
2
(i) 10x
− x − 1 = 0
2
(ii) 5x
Solution
− 2 x + p = 0 has real roots.
Q The equation 10 x
2
(a)
∴ ∆ ≥ 0
− 4(10)( p ) ≥ 0
2
(−2)
4 − 40 p ≥ 0
1
p ≤
10
p = 1
(b) (i)
1
>
10
∴ The equation 10 x
− 2 x + 1 = 0 has no real roots.
2
− x − 1 = 0 by 2, we have
2
(ii)
Multiplying both sides of the equation 5 x
− 2 x − 2 = 0
2
10 x
p = −2
1
≤
10
∴ The equation 5 x
− x − 1 = 0 has real roots.
2
17
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education