Multiple choice

In each of the following questions, two equations (I) and (II) are given. You have to solve them and state the correct relationship-(\text{I.}) (8x^2 + 12x - 8 = 0)(\text{II.}) (9y^2 + 18y + 9 = 0)

  1. $\(x > y\)$
  2. $\(x \ge y\)$
  3. $\(x \le y\)$
  4. $\(x < y\)$

  5. x = y or the relationship can not be established.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solving equation I: 8x² + 12x - 8 = 0. Divide by 4: 2x² + 3x - 2 = 0 gives (2x-1)(x+2) = 0, so x = 1/2 or x = -2. Solving equation II: 9y² + 18y + 9 = 0. Divide by 9: y² + 2y + 1 = 0 gives (y+1)² = 0, so y = -1. Comparing: When x = 1/2, x > y. When x = -2, x < y. Since x can be greater or less than y depending on which root we take, the relationship cannot be established uniquely.

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