Question

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

I. x² - 6x - 40 = 0

II. y² - 7y + 12 = 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 - 6x - 40 = 0

II. y² - 7y + 12 = 0

Calculation:

From I

x² - 6x - 40 = 0

⇒ x² - 10x + 4x - 40 = 0

⇒ x(x - 10) + 4(x - 10) = 0

⇒ (x - 10)(x + 4) = 0

⇒ x = 10, -4

From II

y² - 7y + 12 = 0

⇒ y² - 3y - 4y + 12 = 0

⇒ y(y - 3) - 4(y - 3) = 0

⇒ (y - 3)(y - 4) = 0

⇒ y = 3, 4

Comparison between x and y (via Tabulation)

Value of x	Value of y	Relation between x & y
10	3	x > y
10	4	x > y
-4	3	x < y
-4	4	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