Multiple choice

In the following question, two statements, numbered as I and II are given. On solving them, we get quantities I and II respectively. Solve both the quantities and choose the correct relationship.\n\n\textbf{Quantity I:} $Q_1^2 + 56Q_1 + 783 = 0$\n\textbf{Quantity II:} $Q_2^2 + 46Q_2 + 513 = 0$

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

Solving Q1^2+56Q1+783=0 gives roots Q1=-27 and Q1=-29. Solving Q2^2+46Q2+513=0 gives roots Q2=-27 and Q2=-19. Since both Q1 values (-27, -29) are less than or equal to only one Q2 value (-27), we get Q1 <= Q2.

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