Multiple choice

(\text{In each of these questions, two equations (I) and (II) are given. You have to solve both equations to give the answer :})\n(\text{(I)}\quad x^2 + 15x + 56 = 0 \ \text{(II)}\quad y^2 - 256 = 0)

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

  5. If x = y or no relationship can be established between x and y.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solve equation (I): x² + 15x + 56 = 0 factors to (x+7)(x+8) = 0, giving x = -7 or x = -8. Solve equation (II): y² - 256 = 0 gives y² = 256, so y = ±16 (y = 16 or y = -16). When we compare the values, both possible x values (-7, -8) are less than 16 but greater than -16. This means no definite relationship exists between x and y. For instance, if x = -7 and y = -16, then x > y, but if x = -7 and y = 16, then x < y. Since the relationship cannot be uniquely determined, option E is correct.

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