Multiple choice

In each of the following questions two equations are given. Solve these equations and give answer: ( (I) \quad 5x^2 - 20x + 15 = 0 ) ( (II) \quad 3y^2 - 20y + 17 = 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: 5x² - 20x + 15 = 0. Dividing by 5: x² - 4x + 3 = 0, giving x = 1 or x = 3. Solving equation II: 3y² - 20y + 17 = 0. Using quadratic formula: y = [20 ± √(400-204)]/6 = [20 ± √196]/6 = [20 ± 14]/6, giving y = 17/3 ≈ 5.67 or y = 1. Since x can be both less than and greater than y depending on the chosen roots, no consistent relationship can be established.

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