Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. 3x2 + 25x - 28 = 0 Quantity I: x - 5 Quantity II: x2 + 5

  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 No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 3x^2 + 25x - 28 = 0 gives (3x + 28)(x - 1) = 0, so x = 1 or x = -28/3. If x = 1, Q1 = -4, Q2 = 6 (Q1 < Q2). If x = -28/3, Q1 = -43/3, Q2 = 81.11 (Q1 < Q2). In both cases, Q1 < Q2.

AI explanation

Factoring the quadratic equation 3x^2 + 25x - 28 = 0 by splitting the middle term gives (3x + 28)(x - 1) = 0, which yields the roots x = 1 and x = -28/3. For the root x = 1, Quantity I becomes -4 and Quantity II becomes 6, making Quantity I less than Quantity II. For the root x = -28/3, Quantity I becomes roughly -14.33 and Quantity II remains positive, confirming Quantity I is strictly less than Quantity II. Therefore, Quantity I < Quantity II.

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