Multiple choice

In the following question two equations numbered I and II are given. You have to solve both the equations and give answer.(I. x^2 - 5x + 6 = 0 ) (II. y^2 + y - 6 = 0)

  1. $x > y$
  2. $x ≥ y$
  3. $x < y$
  4. $x ≤ y$
  5. x = y, or relation cannot be established

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

Solving equation I gives x² - 5x + 6 = 0, which factors to (x-2)(x-3) = 0, so x = 2 or x = 3. Solving equation II gives y² + y - 6 = 0, which factors to (y+3)(y-2) = 0, so y = -3 or y = 2. Comparing all values: when x = 2, y can be -3 or 2, giving x ≥ y in both cases (2 > -3 and 2 = 2). When x = 3, y can be -3 or 2, giving x > y in both cases (3 > -3 and 3 > 2). Since x is always greater than or equal to y, x ≥ y is the correct answer.