Multiple choice

In each of the following questions, two equations are given. You have to solve them and Give answer- $(I. \quad x^2 – 15x + 56 = 0)$ $(II. \quad 2y^2 – 10y + 12 = 0)$

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or relationship can not be established
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A Correct answer
Explanation

Solve equation I: x^2 - 15x + 56 = (x-7)(x-8) = 0, so x = 7 or 8. Solve equation II: divide by 2 first, then y^2 - 5y + 6 = (y-2)(y-3) = 0, so y = 2 or 3. Comparing all combinations (7 vs 2, 7 vs 3, 8 vs 2, 8 vs 3), in every case x is greater than y, so x > y is always true.

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