Multiple choice

Directions: Equations I and II are given. You have to solve both the equations and give answer. I. 12p2 + 31p + 9 = 0 II. 6q2 - q - 1 = 0

  1. p ≥ q

  2. p < q

  3. p > q

  4. p ≤ q

  5. p = q or relation cannot be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I: 12p^2 + 31p + 9 = 0. Roots are p = (-31 +/- sqrt(961 - 432)) / 24 = (-31 +/- 23) / 24. p = -8/24 = -1/3 or p = -54/24 = -2.25. II: 6q^2 - q - 1 = 0. Roots are q = (1 +/- sqrt(1 + 24)) / 12 = (1 +/- 5) / 12. q = 6/12 = 0.5 or q = -4/12 = -1/3. Comparing: -2.25 <= -1/3 <= 0.5. Thus, p <= q.

AI explanation

For the first equation, 12p squared + 31p + 9 = 0, we find the roots by factoring to get (3p + 1)(4p + 9) = 0, which gives p = -1/3 and p = -9/4. For the second equation, 6q squared - q - 1 = 0, factoring gives (2q - 1)(3q + 1) = 0, resulting in q = 1/2 and q = -1/3. Comparing the values, we have -9/4 < -1/3 < 1/2, meaning p is either less than q or equal to q. Therefore, the established relation is p <= q.

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