Multiple choice

In each of these question two equations numbered I and II are given. You have to solve both the equations and give answer if - I. (p^2 - 15p + 56 = 0) II. (q^2 - 23q + 132 = 0)

  1. p < q

  2. p > q

  3. p ≤ q

  4. p ≥ q

  5. p = q or no relation between p and q can be established
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A Correct answer
Explanation

For equation I: p² - 15p + 56 = 0 factors to (p-7)(p-8) = 0, so p = 7 or 8. For equation II: q² - 23q + 132 = 0 factors to (q-11)(q-12) = 0, so q = 11 or 12. Since the maximum value of p (8) is less than the minimum value of q (11), p is always less than q regardless of which roots are selected. Therefore p < q.

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