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      Question

      If x2 - 3x + 2 is a factor of, x4

      - px2 + q, then (p, q) =
      A (5, 2) Correct Answer Incorrect Answer
      B (5, 4) Correct Answer Incorrect Answer
      C (-5, -4) Correct Answer Incorrect Answer
      D (-5, 4) Correct Answer Incorrect Answer

      Solution

      The factors of x2 - 3x + 2 are (x - 1) and (x - 2) ┬а Let f(x) = x4 - px2 + q Since, f(x) is divisible by (x - 1) and (x - 2) f(1) = 0 and f(2) = 0 f(1) = 14 - p(1)2 + q = 0 f(1) = 1 - p + q = 0 тАж..(1) f(2) = 24 - p(2)2 + q = 0 f(2) = 16 - 4p + q = 0 ------ ( 2 ) Solving (1) and (2), we get p = 5; q = 4

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