Question

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

I.  x² + 7x + 12 = 0

II. y² - 11y + 18 = 0

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

Answer 1

Correct Answer - Option 2 : x < y

I. x² + 7x + 12 = 0

⇒ x² + 4x + 3x + 12 = 0

⇒ x(x + 4) + 3(x + 4) = 0

⇒ (x + 4)(x + 3)= 0

⇒ x = -4, -3

II. y² - 11y + 18 = 0

⇒ y² - 9y - 2y + 18 = 0

⇒ y(y - 9) + 2(y - 9) = 0

⇒ (y - 9)(y - 2) = 0

⇒  y = 9, 2

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
-4	9	x < y
-4	2	x < y
-3	9	x < y
-3	2	x < y

∴ x < y.