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. 20x2 + 82x + 78 = 0 Quantity I: x2 Quantity II: (x - 1)

  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.
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A Correct answer
Explanation

20x^2 + 82x + 78 = 0. Divide by 2: 10x^2 + 41x + 39 = 0. Factors: (2x + 3)(5x + 13) = 0. Roots: x = -1.5 or x = -2.6. If x = -1.5, Q1 = 2.25, Q2 = -2.5 (Q1 > Q2). If x = -2.6, Q1 = 6.76, Q2 = -3.6 (Q1 > Q2). In both cases, Q1 > Q2.

AI explanation

Use the factorization method to split the middle term of 20x^2 + 82x + 78 = 0 into 60x and 22x, yielding (10x + 13)(2x + 6) = 0. The roots are x = -1.3 and x = -3. For x = -1.3, Quantity I is 1.69 and Quantity II is -2.3; for x = -3, Quantity I is 9 and Quantity II is -4. In both cases, Quantity I is greater than Quantity II.

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