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. $I. (x^2 - x - 12 = 0) II. (y^2 + 5y + 6 = 0)$

  1. $\(X > Y\)$
  2. $\(X < Y\)$
  3. $\(X \le Y\)$
  4. $\(X \ge Y\)$

  5. X = Y or the relationship cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solve equation I: x² - x - 12 = 0 factors to (x-4)(x+3) = 0, giving x = 4 or x = -3. Solve equation II: y² + 5y + 6 = 0 factors to (y+2)(y+3) = 0, giving y = -2 or y = -3. When we compare all possible values: x=4 vs y=-2 gives X > Y; x=4 vs y=-3 gives X > Y; x=-3 vs y=-2 gives X < Y; x=-3 vs y=-3 gives X = Y. Since the relationship varies (X can be greater than, less than, or equal to Y depending on which root values we choose), the relationship cannot be established uniquely.

Keep practicing — related questions