Multiple choice

Solve the following equations and determine the relationship between (x) and (y): (I) (x^2 - 4x - 12 = 0) (II) (3y^2 - 8y + 5 = 0)

  1. If x < y

  2. If x > y

  3. If x ≥ y

  4. If x ≤ y

  5. If x = y or no relationship can be established between x and y.
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E Correct answer
Explanation

Solve equation (I): x² - 4x - 12 = 0 gives x = -2 or x = 6. Solve equation (II): 3y² - 8y + 5 = 0 gives y = 1 or y = 5/3. Comparing values: when x = -2, x < y (since both y values are positive); when x = 6, x > y (since both y values are less than 6). Since the relationship changes depending on which roots we compare, no consistent relationship can be established.

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