Multiple choice

Directions: In the given question, two quantities are given, one as Quantity I and another as Quantity II. You have to determine the relationship between the two quantities and choose the appropriate option. 2x2 + 27x - 45 = 0 Quantity I: x + 7 Quantity II: x2 + 7

  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 relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving 2x^2 + 27x - 45 = 0: (2x - 3)(x + 15) = 0. Roots are x = 1.5 or x = -15. If x = 1.5, Q1 = 8.5, Q2 = 9.25. If x = -15, Q1 = -8, Q2 = 232. In both cases, Q1 < Q2.

AI explanation

Use the factorization method to split the middle term of 2x^2 + 27x - 45 = 0 into 30x and -3x, yielding (2x + 30)(x - 3/2) = 0. The roots are x = -15 and x = 3/2. For the root 3/2, Quantity I evaluates to 17/2 and Quantity II evaluates to 73/4, making Quantity I < Quantity II; for the root -15, Quantity I evaluates to -8 and Quantity II evaluates to 232, making Quantity I < Quantity II. Therefore, Quantity I is always less than Quantity II.

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