Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and then choose the correct option. I. 6p2 – 5p + 1 = 0 II. 4q2 – 7q + 3 = 0

  1. p > q

  2. p ≥ q

  3. p < q

  4. p ≤ q

  5. p = q or no relation can be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: 6p^2 - 5p + 1 = 0 => (2p-1)(3p-1) = 0 => p = 1/2, 1/3. II: 4q^2 - 7q + 3 = 0 => (4q-3)(q-1) = 0 => q = 3/4, 1. Comparing: 1/2 < 3/4, 1/2 < 1, 1/3 < 3/4, 1/3 < 1. Thus, p < q.

AI explanation

Factoring the first quadratic equation 6p^2 - 5p + 1 = 0 yields (2p - 1)(3p - 1) = 0, giving the roots p = 1/2 and p = 1/3. Factoring the second quadratic equation 4q^2 - 7q + 3 = 0 yields (4q - 3)(q - 1) = 0, giving the roots q = 3/4 and q = 1. Comparing these values shows that both values of p (1/3 and 1/2) are strictly less than both values of q (3/4 and 1), establishing the relation p < q.

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