Multiple choice

In each of the following questions, two equations (I) and (II) are given. You have to solve them and answer the given question. $I. (20x^{2} - x - 12 = 0) II. (20y^{2} + 27y + 9 = 0)$

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or relationship cannot be established.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solve equation I: 20x² - x - 12 = 0 using quadratic formula gives x = [1 ± sqrt(1 + 960)]/40 = [1 ± 31]/40, so x = 0.8 or x = -0.75. Solve equation II: 20y² + 27y + 9 = 0 gives y = [-27 ± sqrt(729 - 720)]/40 = [-27 ± 3]/40, so y = -0.6 or y = -0.75. Since the equations share one common root (-0.75) but have different second roots, the relationship between x and y cannot be uniquely established.

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