Multiple choice

(\text{In each of the following questions two equations are given. You have to solve them and give answer -}) (\text{(I)}\quad a^2 - 8a + 15 = 0 )(\text{(II)}\quad b^2 - 5b = -6)

  1. $\(a < b\)$
  2. $\(a > b\)$
  3. $\(a \le b\)$
  4. $\(a \ge b\)$
  5. $\(a = b \text{ or Relationship cannot be determined}\)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving a² - 8a + 15 = 0 gives (a-3)(a-5) = 0, so a = 3 or a = 5. Solving b² - 5b = -6 gives b² - 5b + 6 = 0, which factors to (b-2)(b-3) = 0, so b = 2 or b = 3. Comparing: when a=3, b can equal 3; when a=5, b can be 2 or 3. Since a ≥ b in all cases (a equals or exceeds b), option D is correct.

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