Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. $Quantity I: (4x^2 – 9x – 34 = 0) Quantity II: (8y^2 + 34y – 19 = 0)$

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or the relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solving 4x^2 - 9x - 34 = 0: Using quadratic formula, x = [9 ± sqrt(81 + 544)]/8 = [9 ± sqrt(625)]/8 = [9 ± 25]/8. So x = 34/8 = 4.25 or x = -16/8 = -2. Solving 8y^2 + 34y - 19 = 0: y = [-34 ± sqrt(1156 + 608)]/16 = [-34 ± sqrt(1764)]/16 = [-34 ± 42]/16. So y = 8/16 = 0.5 or y = -76/16 = -4.75. Comparing values: x values are 4.25 and -2, y values are 0.5 and -4.75. No consistent relationship can be established (sometimes x > y, sometimes x < y).

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