Question

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

I. x² + 9x + 14 = 0

II. 3y² + 4y + 1 = 0

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

Answer 1

Correct Answer - Option 2 : x < y

I. x2 + 9x + 14 = 0

⇒ x2 + 7x + 2x + 14 = 0

⇒ x (x + 7) + 2 (x + 7) = 0

⇒ (x + 2)(x + 7) = 0

⇒ x = - 2, -7

II. 3y2 + 4y + 1 = 0

⇒ 3y2 + 3y + y + 1 = 0

⇒ 3y(y + 1) + 1(y + 1) = 0

⇒ (3y + 1)(y + 1) = 0

⇒ \(y = - 1, - \frac{1}{3}\)

On comparing the values of x and y,

Value of x	Value of y	Relation
- 2	-1	x < y
- 2	- (1/3)	x < y
- 7	-1	x < y
- 7	- (1/3)	x < y

 

∴ x < y