NCERT Class 10 Mathematics

QUADRATIC EQUATIONS 81

Therefore, the solutions of the equations are

3

2

x and 1.

Let us verify our solutions.

Putting

3

2

x in 2x^2 – 5x + 3 = 0, we get

332

2–5 3 0

22

✁ ✂ ✁ ✂✄ ☎

✆✞ ✝✟ ✆✞ ✝✟ , which is

correct. Similarly, you can verify that x = 1 also satisfies the given equation.

In Example 7, we divided the equation 2x^2 – 5x + 3 = 0 throughout by 2 to get

x^2 –

53

22

x✠ = 0 to make the first term a perfect square and then completed the

square. Instead, we can multiply throughout by 2 to make the first term as 4x^2 = (2x)^2
and then complete the square.

This method is illustrated in the next example.

Example 8 : Find the roots of the equation 5x^2 – 6x – 2 = 0 by the method of completing
the square.

Solution : Multiplying the equation throughout by 5, we get

25 x^2 – 30x – 10 = 0

This is the same as

(5x)^2 – 2 × (5x) × 3 + 3^2 – 3^2 – 10 = 0

i.e., (5x – 3)^2 – 9 – 10 = 0

i.e., (5x – 3)^2 – 19 = 0

i.e., (5x – 3)^2 =19

i.e., 5 x – 3 = ✡ 19

i.e., 5 x = 31 ✡ 9

So, x =

319

5

☛

Therefore, the roots are

319

5

☞

and

319

5

✌

.

Verify that the roots are

319

5

☞ and^319

5

✌.