Question

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

I. 3x² – 7x + 2 = 0

II. 2y² – 11y + 15 = 0

1. x > y
2. x < y
3. x ≥ y
4. x ≤ y

Answer 1

Correct Answer - Option 2 : x < y

I. 3x2 – 7x + 2 = 0

⇒ 3x² – 6x – x + 2 = 0

⇒ 3x (x – 2) – 1 (x – 2) = 0

⇒ (x – 2) (3x – 1) = 0

⇒ x = 2 or 1/3

II. 2y2 – 11y + 15 = 0

⇒ 2y² – 6y – 5y + 15 = 0

⇒ 2y (y – 3) – 5 (y – 3) = 0

⇒ (y – 3) (2y – 5) = 0

⇒ y = 3 or 5/2

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
2	3	x < y
2	5/2	x < y
1/3	3	x < y
1/3	5/2	x < y

∴ Clearly x < y