## Book: RS Aggarwal - Mathematics

### Chapter: 10. Quadratic Equations

#### Subject: Maths - Class 10th

##### Q. No. 58 of Exercise 10A

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58
##### Solve each of the following quadratic equations:

Given:

taking LCM

using (a - b)2 = a2 + b2 - 2ab

cross multiplying

18x2 - 48x + 130 = 105x - 140

18x2 - 153x + 270 = 0 taking 9 common

2x2 - 17x + 30 = 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 a = 2 b = - 17 c = 30

= 2.30 = 60

And either of their sum or difference = b

= - 17

Thus the two terms are - 12 and - 5

Sum = - 12 - 5 = - 17

Product = - 12. - 5 = 60

2x2 - 17x + 30 = 0

2x2 - 12x - 5x + 30 = 0

2x(x - 6) - 5(x - 6) = 0

(x - 6) (2x - 5) = 0

(x - 6) = 0 or (2x - 5) = 0

Hence the roots of equation are

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
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17
18
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21
22
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25
26
27
28
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30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
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46
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48
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51
52
53
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55
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58
59
60
61
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73