Multiple choice

Directions: In the following question, equations numbered I and II are given. You have to solve both the equations and choose the correct option. I. 22p2 + 5p - 3 = 0 II. 6q2 - 43q + 77 = 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: 22p^2 + 5p - 3 = 0. Roots are p = [-5 +/- sqrt(25 - 4*22*-3)] / 44 = [-5 +/- sqrt(289)] / 44 = [-5 +/- 17] / 44. p = 12/44 = 3/11 or p = -22/44 = -0.5. II: 6q^2 - 43q + 77 = 0. Roots are q = [43 +/- sqrt(1849 - 4*6*77)] / 12 = [43 +/- sqrt(1849 - 1848)] / 12 = [43 +/- 1] / 12. q = 44/12 = 11/3 or q = 42/12 = 3.5. Since both values of p are less than both values of q, p < q.

AI explanation

Factoring equation one gives 22p^2 + 11p - 6p - 3 = 0, which becomes (2p + 1)(11p - 3) = 0, yielding p = -0.5 or p = 3/11. Factoring equation two gives 6q^2 - 14q - 29q + 77 = 0, which becomes 2q(3q - 7) - 11(3q - 7) = 0, yielding q = 11/2 or q = 7/3. Since both values of p are less than both values of q, p < q.

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