Correct Answer - Option 2 : x < y
Given:
I. 6x2 + 19x - 25 = 0
II. y2 - 10y + 24 = 0
Calculation:
From I,
6x2 + 19x - 25 = 0
⇒ 6x2 + 25x - 6x - 25 = 0
⇒ x(6x + 25) - 1(6x + 25) = 0
⇒ (6x + 25)(x - 1) = 0
Taking,
⇒ (6x + 25) = 0 or (x - 1) = 0
⇒ x = (-25/6) or 1
From II,
y2 - 10y + 24 = 0
⇒ y2 - 6y - 4y + 24 = 0
⇒ y(y - 6) - 4(y - 6) = 0
⇒ (y - 6)(y - 4) = 0
Taking,
⇒ (y - 6) = 0 or (y - 4) = 0
⇒ y = 6 or 4
Comparison between x and y (via Tabulation):
Value of x
|
Value of y
|
Relation
|
-25/6
|
6
|
x < y
|
-25/6
|
4
|
x < y
|
1
|
6
|
x < y
|
1
|
4
|
x < y
|
∴ x < y.