Correct Answer - Option 2 : x < y
Given:
I. x2 + 6x + 5 = 0
II. 8y2 - 22y - 21 = 0
Concept used:
Using quadratic equation.
Calculation:
From I,
x2 + 6x + 5 = 0
⇒ x2 + 5x + x + 5 = 0
⇒ x(x + 5) + 1(x + 5) = 0
⇒ (x + 5)(x+1) = 0
⇒ x = - 5, -1
From II,
8y2 - 22y - 21 = 0
⇒ 8y2 - 28y + 6y - 21 = 0
⇒ 4y(2y - 7) + 3(2y - 7) = 0
⇒ (2y - 7)(4y + 3) = 0
⇒ y = 7/2, - 3/4
Comparison between x and y (via Tabulation):
Value of x
|
Value of y
|
Relation
|
-5
|
7/4 |
x < y
|
-5
|
-3/4
|
x < y
|
- 1
|
7/4
|
x < y
|
- 1
|
-3/4
|
x < y
|
∴ x < y.