Multiple choice

In each of the following question, two equations are given. You have to solve them and give answer. I. (p^2 + 24 = 10p) II. (2q^2 + 18 = 12q)

  1. If p < q

  2. If p > q

  3. If p ≤ q

  4. If p ≥ q

  5. If p = q or relation between p and q cannot be established.
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B Correct answer
Explanation

For p^2 + 24 = 10p, rearranging gives p^2 - 10p + 24 = 0, which factors to (p-4)(p-6) = 0, so p = 4 or p = 6. For 2q^2 + 18 = 12q, dividing by 2 gives q^2 - 6q + 9 = 0, which is (q-3)^2 = 0, so q = 3. Since both possible values of p (4 and 6) are greater than q = 3, we have p > q.

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