Correct Answer  Option 2 : x < y
Calculation:
From I,
3x2 + 16x + 21 = 0
⇒ 3x2 + 9x + 7x + 21 = 0
⇒ 3x(x + 3) + 7(x + 3) = 0
⇒ (x + 3)(3x + 7) = 0
Taking,
⇒ x + 3 = 0 or 3x + 7 = 0
⇒ x = – 3 or x = – 7/3
From II,
6y2 + 17y + 12 = 0
⇒ 6y2 + 9y + 8y + 12 = 0
⇒ 3y(2y + 3) + 4(2y + 3) = 0
⇒ (3y + 4)(2y + 3) = 0
Taking,
⇒ 2y + 3 = 0 or 3y + 4 = 0
⇒ y = – 3/2 or y = – 4/3
Comparison between x and y (via Tabulation):
x

Y

Relation

– 3

– 3/2

x < y

– 3

– 4/3

x < y

– 7/3

– 3/2

x < y

– 7/3

– 4/3

x < y

∴ After comparing x and y both, x < y.