Multiple choice

Directions: In this question, two equations (I) and (II) are given. You have to solve both the equations and give the answer. (I) 2p2 + p - 3 = 0 (II) 6q2 = 15q - 9

  1. p > q

  2. p < q

  3. p ≥ q

  4. p ≤ q

  5. p = q, or no relation can be established between 'p' and 'q'.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Equation I: 2p^2 + p - 3 = 0. (2p+3)(p-1) = 0. p = 1, -1.5. Equation II: 6q^2 - 15q + 9 = 0. 2q^2 - 5q + 3 = 0. (2q-3)(q-1) = 0. q = 1.5, 1. Comparing roots: p can be 1 or -1.5, q can be 1.5 or 1. Thus p <= q.

AI explanation

Solving the first equation 2p2 + p - 3 = 0 by factoring gives (2p + 3)(p - 1) = 0, so the roots are p = -3/2 and p = 1. For the second equation, 6q2 - 15q + 9 = 0, dividing by 3 gives 2q2 - 5q + 3 = 0, which factors into (2q - 3)(q - 1) = 0, yielding the roots q = 3/2 and q = 1. Comparing the roots, we have -1.5 less than 1.5, 1 equal to 1, and 1 less than 1.5. Every possible value of p is less than or equal to a corresponding value of q, establishing the relation p ≤ q.

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