Multiple choice

In each question two equations numbered I and II are given, you have to solve both the equation and choose the correct answer. I. (x^2 + 42x + 405 = 0) II. (y^2 + 45y + 506 = 0)

  1. $\(x > y\)$
  2. $\(x < y\)$
  3. $\(x \le y\)$
  4. $\(x \ge y\)$
  5. $\(x = y\) or the relationship can’t be established$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solving equation I: x² + 42x + 405 = 0. Using quadratic formula: x = (-42 ± √(1764-1620))/2 = (-42 ± √144)/2 = (-42 ± 12)/2. So x = -15 or x = -27. Solving equation II: y² + 45y + 506 = 0 gives y = (-45 ± √(2025-2024))/2 = (-45 ± 1)/2. So y = -22 or y = -23. Comparing: -15 > -22 (x > y), -15 > -23 (x > y), -27 < -22 (x < y), -27 < -23 (x < y). Since x can be greater or less than y, the relationship cannot be established.

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