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 - 16x + 63 = 0

II. y² + 5y - 84 = 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 3 : x ≥ y

Given:

I. x² - 16x + 63 = 0

II. y² + 5y - 84 = 0

Calculation:

From I

x² - 16x + 63 = 0

⇒ x² - 9x - 7x + 63 = 0

⇒ x(x - 9) - 7(x - 9) = 0

⇒ (x - 9)(x - 7) = 0

⇒ x = 9, 7

From II

y² + 5y - 84 = 0

⇒ y² + 12y - 7y -84 = 0

⇒ y(y + 12) - 7(y + 12) = 0

⇒ (y + 12)(y - 7) = 0

⇒ y = -12, 7

Comparison between x and y (via Tabulation)

Value of x	Value of y	Relation between x & y
9	-12	x > y
9	7	x > y
7	-12	x > y
7	7	x = y

∴ 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