(Q2)find the roots of 4x2 + 3x + 5 = 0 by method of completing the square.

Answer:

Given: 4x2 + 3x + 5 = 0

x2 +
3
4
x +
5
4
 = 0

x2 +
3
4
x =
-5
4

x2 +
3
4
x + (
3
8
)2 =
-5
4
 + (
3
8
)2

(x +
)2 =
-5
4
 +
64

(x +
)2 =
-
64
 < 0

But (x +
)2 cannot be negative for any real value of x.(Why?) So, there is no real value of x satisfying the given equation. therefore, the given equation has no real roots.