Question

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

I. 2x² + 10x + 8 = 0

II. 3y²– 2y – 5 = 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 3 : x ≤ y

Calculation:

From I,

2x² + 10x + 8 = 0

⇒ 2x² + 8x + 2x + 8 = 0

⇒ 2x(x+4) + 2(x+4) = 0

⇒ (2x+2) (x+4) = 0

Taking, 

⇒ 2x + 2 = 0 or x + 4 = 0

⇒ x = –1, –4

From II,

3y²– 2y – 5 =0

⇒ 3y² + 3y – 5y – 5 = 0

⇒ 3y(y+1) –5(y+1) = 0

⇒ (3y–5) (y+1) = 0

Taking,

⇒ 3y – 5 = 0 or y + 1 = 0

⇒ y = 5/3, –1

Values of x	Values of y	Relation
–1	5/3	x < y
–4	5/3	x < y
–1	–1	x = y
–4	–1	x < y

∴ Relation between x and y is, x ≤ y.