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 |