NCERT Class 10 Mathematics

QUADRATIC EQUATIONS 79

So, 9x^2 – 15x + 6 = 0 can be written as

512

3

24

✄ x✂ ✁☎ ✂

✆ ✝

=0

i.e.,

5 2

3

2

✞✡ x✠ ✟☛

☞ ✌

=

1

4

So, the solutions of 9x^2 – 15x + 6 = 0 are the same as those of

512

3

24

✄ x✂ ✁☎ ✍

✆ ✝

.

i.e., 3 x –

5

2

=

1

2

or

3 5

2

x✎ =^1

2

✎

(We can also write this as

3 51

22

x✏ ✑✒ , where ‘✓’ denotes ‘plus minus’.)

Thus, 3 x =

51

22

✔ or 3 51

22

x✕ ✎

So, x =

51

66

✖ or^51

66

x✑ ✏

Therefore, x = 1 or x =

4

6

i.e., x = 1 or x =

2

3

Therefore, the roots of the given equation are 1 and

(^2).
3
Remark : Another way of showing this process is as follows :
The equation 3 x^2 – 5x + 2 = 0
is the same as
2 52
33
xx✏ ✖ =0
Now, x^2 –

52

33

x✖ =

22

15 15 2

23 23 3

✢✗x✛ ✤✙ ✥✚✘✣ ✛✢✗ ✙✤ ✚✥✣✘ ✜

★ ✦ ✧✩ ★ ✦ ✧✩