## Book: RS Aggarwal - Mathematics

#### Subject: Maths - Class 10th

##### Q. No. 3 of Exercise 10A

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

3
##### Find the value of k for which x = 1 is a root of the equation x2 + kx + 3 = 0. Also, find the other root.

Given x = 1 is a root of the equation x2 + kx + 3 = 0 it means it satisfies the equation.

Substituting x = 1 in equation -

12 + k(1) + 3 = 0

Putting the value of k in the given equation : x2 + kx + 3 = 0

This reduced to the quadratic equation x2 - 4x + 3 = 0

Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation

= 1.3

= 3

And either of their sum or difference = b

= - 4

Thus the two terms are - 1 and - 3

Sum = - 1 - 3 = - 4

Product = - 1. - 3 = 3

x(x-1)-3(x-1) = 0

(x-1)(x-3) = 0

x = 1 or x = 3

Thus other root is 3.

1
1
1
1
1
1
1
1
1
1
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
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73