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      Question

      I. x2 – 9x + 18 = 0 II.

      y2 – 5y + 6 = 0 In each question two equations numbered (I) and (II) are given. You should solve both the equations and mark appropriate answer.
      A if x > y Correct Answer Incorrect Answer
      B if x ≥ y Correct Answer Incorrect Answer
      C if x < y Correct Answer Incorrect Answer
      D if x ≤ y Correct Answer Incorrect Answer
      E if x = y or the relation between x and y cannot be established Correct Answer Incorrect Answer

      Solution

      I. x2 – 9x + 18 = 0
      => x2 – 6x – 3x + 18 = 0
      => x (x – 6) – 3(x – 6) = 0
      => x = 6, 3
      II. y2 – 5y + 6 = 0
      => y2 – 3y - 2y + 6 = 0
      => y (y – 3) - 2 (y – 3) = 0
      => y = 3, 2
      Hence, x ≥ y
      Alternate Method:
      if signs of quadratic equation is - ve and +ve then the roots of equation will be +ve and +ve.
      So, x = 6, 3
      y = 3, 2
      After comparing we can conclude that x ≥ y.

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