Question

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

I. x² − 12x − 108 = 0

II. y² + 19y + 78 = 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 3 : x ≥ y

I. x2 − 12x − 108 =0

⇒ x2 − 18x + 6x − 108  = 0

⇒ x(x − 18) + 6(x − 18) = 0

⇒ (x + 6), (x − 18) = 0

x = − 6, 18

 

II. y2 + 19y + 78 = 0

⇒ y2 + 13y + 6y + 78 = 0

⇒ y(y + 13) + 6(y + 13) = 0

 y = − 13,  − 6

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
- 6	- 6	x = y
- 6	- 13	x > y
18	- 6	x > y
18	- 13	x > y

∴ x ≥ y