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      Question

      Solve the quadratic equations and determine the relation

      between x and y: Equation 1: 4x┬▓ - 12x + 9 = 0 Equation 2: 2y┬▓ + 8y + 6 = 0
      A x > y Correct Answer Incorrect Answer
      B x тЙе y Correct Answer Incorrect Answer
      C x < y Correct Answer Incorrect Answer
      D x тЙд y Correct Answer Incorrect Answer
      E No relation Correct Answer Incorrect Answer

      Solution

      From equation 1: 4x┬▓ - 12x + 9 = 0 Dividing by 4: x┬▓ - 3x + 2.25 = 0 Discriminant: (-3)┬▓ - 4(1)(2.25) = 9 - 9 = 0 (double root). Roots: x = 3 / 2 = 1.5 (double root). From equation 2: 2y┬▓ + 8y + 6 = 0 Dividing by 2: y┬▓ + 4y + 3 = 0 Factorizing: (y + 3)(y + 1) = 0 So, y = -3 or y = -1. Comparing x and y: ┬аIf x = 1.5 and y = -3, x > y. ┬аIf x = 1.5 and y = -1, x > y. Thus, x > y. Answer: A

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