Question

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

I.  7x² + 15x + 8 = 0

II.  y² + y/2 – 1/2 = 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 4 : x ≤ y

I. 7x² + 15x + 8 = 0

⇒ 7x² + 7x + 8x + 8 = 0

⇒ 7x(x + 1) + 8(x + 1) = 0

⇒ (7x + 8)(x + 1) = 0

⇒ x = -8/7, -1

II. y² + y/2  – 1/2 = 0

⇒ y² + y – 1/2y – 1/2 = 0

⇒ y(y + 1) – 1/2(y + 1) = 0

⇒ (y – 1/2)(y + 1) = 0

⇒ y = 1/2, -1

Value of x	Value of y	Relation
-8/7	1/2	X < y
-8/7	-1	X < y
-1	1/2	X < y
-1	-1	X = y

∴ x ≤ y