Question

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. 3x² + 5x + 2 = 0

II. 3y² + 18y + 24 = 0

1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. x = y or relationship between x and y cannot be established

Answer 1

Correct Answer - Option 1 : x > y

I. 3x2 + 5x + 2 = 0

⇒ 3x² + 3x + 2x + 2 = 0

⇒ 3x (x + 1) + 2 (x + 1) = 0

⇒ (3x + 2) (x + 1) = 0

⇒ x = –2/3 or –1

II. 3y2 + 18y + 24 = 0 

⇒ y² + 6y + 8 = 0

⇒ y² + 4y + 2y + 8 = 0

⇒ y (y + 4) + 2 (y + 4) = 0

⇒ (y + 2) (y + 4) = 0

⇒ y = –2 or –4

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
-2/3	-2	x > y
-2/3	-4	x > y
-1	-2	x > y
-1	-4	x > y

∴ Clearly x > y