Multiple choice

In each of the following questions two equations are given. Solve these equations and give answer : ( (I) \quad x^{2} – 19x +34 = 0 ) ( (II) \quad y^{2} – 23y +120 = 0 )

  1. If x < y

  2. If x > y

  3. If x ≥ y

  4. If x ≤ y

  5. If x = y or no relationship can be established between x and y.
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E Correct answer
Explanation

Solving equation (I) using quadratic formula: x = [19 ± √(361-136)]/2 = [19 ± √225]/2 = [19 ± 15]/2, giving x = 17 or x = 2. Solving equation (II): y = [23 ± √(529-480)]/2 = [23 ± √49]/2 = [23 ± 7]/2, giving y = 15 or y = 8. When x = 17, x > y (for both y = 15 and y = 8). When x = 2, x < y (for both y = 15 and y = 8). Since x can be greater or less than y depending on which root we select, no consistent relationship can be established.

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