Question

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

I. 5x2 + 28x - 12 = 0

II. y2 - 13y + 40 = 0

1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. x = y or relation between x and y can not be established.

Answer 1

Correct Answer - Option 2 : x < y

Given: 

I. 5x2 + 28x - 12 = 0

II. y2 - 13y + 40 = 0

Calculation:

From I,

5x2 + 28x - 12 = 0

⇒ 5x2 + 30x - 2x - 12 = 0

⇒ 5x(x + 6) - 2(x + 6) = 0

⇒ (x + 6)(5x - 2) = 0

Taking,

⇒ (x + 6) = 0 or  (5x - 2) = 0

⇒ x = -6 or (2/5)

From II,

y2 - 13y + 40 = 0

⇒ y2 - 8y - 5y + 40 = 0

⇒ y(y - 8) - 5(y - 8) = 0

⇒ (y - 8)(y - 5) = 0

Taking,

⇒ (y - 8) = 0 or (y - 5) = 0

⇒ y = 8 or 5

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
-6	8	x < y
-6	5	x < y
2/5	8	x < y
2/5	5	x < y

∴ x < y.