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. \text{Quantity I:} 7x^2 – 34x - 5 = 0 \text{Quantity II:} 2y^2 – 3y - 14 = 0

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity II ≤ 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

Quantity I: 7x² - 34x - 5 = 0 factors to (7x+1)(x-5)=0, giving x = -1/7 or x = 5. Quantity II: 2y² - 3y - 14 = 0 factors to (2y+7)(y-2)=0, giving y = -3.5 or y = 2. Comparing roots: max(x) = 5, max(y) = 2, so x > y for maximum. But min(x) = -1/7 ≈ -0.14, min(y) = -3.5, so x > y for minimum too. Actually comparing individual roots: 5 > 2 (yes), -1/7 > -3.5 (yes). So x > y always? Wait, we need to compare both roots. If x = -1/7 and y = 2, then x < y. If x = 5 and y = -3.5, then x > y. No consistent relationship. Option E is correct.

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