Question

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

I. 10x² + 33x + 27 =0

II. 5y² + 19y + 18 = 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. 10x2 + 33x + 27 = 0

⇒ 10x² + 15x + 18x + 27 = 0

⇒ 5x(2x + 3) + 9(2x + 3) = 0

⇒ (2x + 3) (5x + 9) = 0

x = − 3/2 or − 9/5

 

II. 5y2 + 19y + 18 = 0  

⇒ 5y² + 10y + 9y + 18 = 0

⇒ 5y (y + 2) + 9 (y + 2) = 0

⇒ (y + 2) (5y + 9) = 0

y = −2 or − 9/5

 

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
-3/2	-2	x > y
-3/2	-9/5	x > y
-9/5	-2	x > y
-9/5	-9/5	x = y

 

∴ x ≥ y