Multiple choice

(\text{In the following question two equations are given. You have to solve them and give answer -}\ (\text{(I)}) \quad p^2 + p - 42 = 0\ (\text{(II)}) \quad q^2 + 11q + 30 = 0

  1. If p < q

  2. If p > q

  3. If p ≤ q

  4. If p ≥ q

  5. If p = q or relation can't be established.
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E Correct answer
Explanation

Equation (I): p² + p - 42 = 0 factors as (p+7)(p-6) = 0, giving p = -7 or p = 6. Equation (II): q² + 11q + 30 = 0 factors as (q+5)(q+6) = 0, giving q = -5 or q = -6. Comparing all values: When p = -7, p < q (for both q = -5, -6). When p = 6, p > q (for both q = -5, -6). Since p can be less or greater than q, the relation cannot be uniquely established.

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