Question

In the given questions, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer.

I. x² - 12x + 36 = 0

II. y² - 7y - 60 = 0

1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. No relation in x and y or x = y

Answer 1

Correct Answer - Option 5 : No relation in x and y or x = y

Given:

I. x2 - 12x + 36 = 0

II. y2 - 7y - 60 = 0

Calculation:

From I

x2 - 12x + 36 = 0

⇒ x² - 6x - 6x + 36 = 0

⇒ x(x - 6) - 6(x - 6) = 0

⇒ (x - 6)(x - 6) = 0

⇒ x = 6, 6

From II

y2 - 7y - 60 = 0

⇒ y² - 12y + 5y - 60 = 0

⇒ y(y - 12) + 5(y - 12) = 0

⇒ (y - 12)(y + 5) = 0

⇒ y = 12, -5

Comparison between x and y (via Tabulation)

Value of x	Value of y	Relation between x & y
6	12	x < y
6	-5	x > y
6	12	x < y
6	-5	x > y

∴ No relation in x and y or x = y.

Sign Method
Equation	Sign	Remark
ax2 + bx + c = 0	-Ve, -Ve	Same signs
ax2 - bx + c = 0	+Ve, +Ve	Same signs
ax2 + bx - c = 0	-Ve, +Ve	Larger root is negative smaller root is positive
ax2 - bx - c = 0	-Ve, +Ve	Larger root is positive smaller root is negative