NCERT Class 10 Mathematics

86 MATHEMATICS

Example 14 : Find the roots of the following equations:

(i)

1

xx3, 0

x

 ✁ ✂ (ii)

11

3, 0, 2

2

x

x x

✄ ✁ ✂

✄

Solution :

(i)

1

x 3

x

☎ ✆. Multiplying throughout by x, we get

x^2 + 1 = 3x

i.e., x^2 – 3x + 1 = 0, which is a quadratic equation.

Here, a = 1, b = – 3, c = 1

So, b^2 – 4ac = 9 – 4 = 5 > 0

Therefore, x =

35

2

✝

(Why?)

So, the roots are

35 35

and

22

✞ ✟

.

(ii)

11

3, 0, 2

2

x

x x

✄ ✁ ✂

✄

.

As x ✠ 0, 2, multiplying the equation by x (x – 2), we get

(x – 2) – x =3x (x – 2)

=3x^2 – 6x

So, the given equation reduces to 3x^2 – 6x + 2 = 0, which is a quadratic equation.

Here, a = 3, b = – 6, c = 2. So, b^2 – 4ac = 36 – 24 = 12 > 0

Therefore, x =

61262333

.

663

✡ ✡ ✡

☛ ☛

So, the roots are

33 33

and

33

✞ ✟

.