Multiple choice

Find the value of variables and state the correct relationship.(x^2 + 2x - 15 = 0)(y^2 - y - 20 = 0)

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

  5. x=y or relation cannot be established
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E Correct answer
Explanation

x² + 2x - 15 = 0 factors to (x+5)(x-3) = 0, so x = -5 or x = 3. y² - y - 20 = 0 factors to (y-5)(y+4) = 0, so y = -4 or y = 5. Comparing all pairs: -5 < -4, -5 < 5, 3 > -4, 3 < 5. Since x can be less than, greater than, or equal to y depending on which roots we compare, no unique relationship exists.

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