Multiple choice

In this question two equations numbered I and II are given. You have to solve both the equations and mark the appropriate option.\newline I. (2p^2 + 11p + 12 = 0)\newline II. (6q^2 - 31q + 40 = 0)

  1. If p < q

  2. If p ≥ q

  3. If p ≤ q

  4. If p > q

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

For equation I: 2p² + 11p + 12 = 0 factors as (2p + 3)(p + 4) = 0, giving p = -1.5 or p = -4. For equation II: 6q² - 31q + 40 = 0. Using the quadratic formula: q = (31 ± √(961 - 960))/12 = (31 ± 1)/12, giving q = 8/3 ≈ 2.67 or q = 5/2 = 2.5. Comparing the values: all p values (-1.5, -4) are less than all q values (2.67, 2.5). Therefore p < q.

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