(Q12)Find the roots of the following quadratic equation, if they exist, by the method of completing the square.

(i) 2x2 + x - 4 = 0

Answer:

Given: 2x2 + x - 4 = 0

2x2 + x = 4

(√2x)2 + x = 4

(√2x)2 + 2.√ 2.x.
1
2√2
 = 4

Now LHS is in the form a2 + 2ab

where b =
1
2√2
Adding b2 = (
1
2√2
 )2on both sides we get

(√2x)2 + 2√2x.
1
2√2
 + (
1
2√2
 )2
= 4 + (
1
2√2
)2

(√2x +
1
2√2
 )2= 4 +
1
4×2
 =
8

(√2x +
1
2√2
 )2 =
8

∴ √2x +
1
2√2
 = √
8
 = ±
√
2√2

∴ √2x = ± (
√
2√2
) - (
1
2√2
)

x =
√
 -
1
 or
-√
 -
1

x =
√-1
 or
-√-1

∴ The roots are
-1+√
 and
-1-√