Question

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

I. 3x² + 2x – 1 = 0

II. 11y² + 18y + 7 = 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 5 : x = y or the relationship between x and y cannot be established.

Calculation:

From I,

3x ² + 2x – 1 = 0

⇒ 3x² + 3x – x – 1 = 0

⇒ 3x(x + 1) – 1(x + 1) = 0

⇒ (3x – 1)(x + 1) = 0

Taking, 

⇒ 3x – 1 = 0 or x + 1 = 0

⇒ x = 1/3 or x = –1

 

From II,

11y² + 18y + 7 = 0 

⇒ 11y² + 11y + 7y +7 = 0

⇒ 11y(y + 1) + 7(y + 1) = 0

⇒ (y + 1)(11y + 7) = 0

Taking, 

⇒ y + 1 = 0 or 11y + 7 = 0

⇒ y = –1 or y = –7/11

Comparison between x and y (via Tabulation)

Value of x	Value of y	Relation
1/3	–1	x > y
1/3	–7/11	x > y
–1	–1	x = y
–1	–7/11	x < y

 

∴x = y or the relationship between x and y cannot be established.