Directions: In each of the following questions, two equations numbered (I) and…
2020
Directions: In each of the following questions, two equations numbered (I) and (II) are given. Solve both equations and choose the correct relationship between x and y.
I. x² - 17x – 84 = 0
II. y² + 4y – 117 = 0
- A.
If x > y
- B.
If x ≥ y
- C.
If y > x
- D.
If y ≥ x
- E.
If x = y or no relation can be established
Attempted by 5 students.
Show answer & explanation
Correct answer: E
Equation I: x² - 17x - 84 = 0 → (x - 21)(x + 4) = 0, so x = 21 or x = -4.
Equation II: y² + 4y - 117 = 0 → (y + 13)(y - 9) = 0, so y = 9 or y = -13.
Now compare every value of x with every value of y:
• x = 21, y = 9 → x > y • x = 21, y = -13 → x > y • x = -4, y = 9 → x < y • x = -4, y = -13 → x > y
Some pairs give x > y while one pair gives x < y, so no single, consistent relationship holds for all roots. Note also that x is never equal to y here. In the standard banking format, the final option “x = y OR no relationship can be established” is the catch-all choice used whenever a fixed relation cannot be determined — it covers both the equality case and the no-relation case. Since this problem falls in the no-relation case, that option is the correct one.