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. I. What is the maximum value of (-5x^2 - 20x + 4)? II. (900x^2 - 54000x + 810000 = 0)

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

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

Quantity I: For quadratic ax² + bx + c where a < 0, maximum value at x = -b/(2a). Here x = -20/(2×-5) = -2. Maximum value = -5(4) - 20(-2) + 4 = 24. Quantity II: 900x² - 54000x + 810000 = 0 simplifies to x² - 60x + 900 = 0, giving x = 30. Since 24 < 30, Quantity II > Quantity I.

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