Multiple choice

(\text{Solve both the quantities and state the correct relationship.}\\text{Quantity I:} 3Q_1^2 + 168Q_1 + 2349 = 0\\text{Quantity II:} 2Q_2^2 + 92Q_2 + 1026 = 0)

  1. $\(Q_1 > Q_2\)$
  2. $\(Q_1 \ge Q_2\)$
  3. $\(Q_1 < Q_2\)$
  4. $\(Q_1 \le Q_2\)$
  5. $\(Q_1 = Q_2 \text{ or relationship cannot be established}\)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For Q1: 3x² + 168x + 2349 = 0. Discriminant = 168² - 4(3)(2349) = 28224 - 28188 = 36. Roots = (-168 ± 6)/6 = -27.5, -28.5. For Q2: 2x² + 92x + 1026 = 0. Discriminant = 92² - 4(2)(1026) = 8464 - 8208 = 256. Roots = (-92 ± 16)/4 = -23, -27. Both Q1 roots (-27.5, -28.5) are less than both Q2 roots (-23, -27). Therefore, Q1 ≤ Q2.

Keep practicing — related questions