Multiple choice

In each of the following questions, two equations are given. You have to solve them and $( (I) \quad x^2 + 12x + 27 = 0 \ (II) \quad y^2 + 11y + 30 = 0 )$

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or relationship can not be established

Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solve equation (I): x^2 + 12x + 27 = 0 factors to (x+3)(x+9) = 0, giving x = -3 or x = -9. Solve equation (II): y^2 + 11y + 30 = 0 factors to (y+5)(y+6) = 0, giving y = -5 or y = -6. When x = -3, x > y for both y values. When x = -9, x < y for both y values. Since x can be greater or less than y depending on which root you choose, no single relationship can be established.