Multiple choice

Directions: Equations I and II are given. You have to solve both the equations and give answer. I. 11p2 + 40p + 21 = 0 II. 11q2 - 15q - 14 = 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: 11p^2 + 40p + 21 = 0. Roots: p = (-40 +/- sqrt(1600 - 924))/22 = (-40 +/- 26)/22. p = -14/22 = -7/11 or p = -66/22 = -3. II: 11q^2 - 15q - 14 = 0. Roots: q = (15 +/- sqrt(225 + 616))/22 = (15 +/- 29)/22. q = 44/22 = 2 or q = -14/22 = -7/11. Comparing: p <= q.

AI explanation

Factor the first quadratic 11p^2 + 40p + 21 = 0 to find its roots, which are -7/11 and -3. Factoring the second quadratic 11q^2 - 15q - 14 = 0 gives the roots 2 and -7/11. Comparing the sets shows that both equations share the root -7/11, while the other root of q (which is 2) is strictly greater than the other root of p (which is -3). Therefore, every value of p is either equal to -7/11 or strictly less than 2, establishing the relationship p <= q.

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