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      Question

      Find the values of 'a' and 'b', so that the polynomial

      x3 − ax2 − 13x + b has (x−1) and (x+3) as factors:
      A a = 4, b = 5 Correct Answer Incorrect Answer
      B a = 3, b = 15 Correct Answer Incorrect Answer
      C a = 15, b = 3 Correct Answer Incorrect Answer
      D a = 5, b = 4 Correct Answer Incorrect Answer

      Solution

      Let (p(x)) = x3 − ax2 − 13x + b If (x - 1) and (x + 3) are factors of p(x), then p (l) = O and p (- 3) = O (1)3 − a(1)2 – 13 x 1 + b = 0 and (−3)3 − a(−3)2 − 13(−3) + b = 0 1 − a – 13 + b = 0 and −27– 9a+ 39 + b = 0 a – b = - 12 …..(1) and 9a – b = 12 …..(2) Subtracting the equation from first, we get (a - b) - (9a - b) = - 12 - 12 - 8a = - 24 a = 3 Putting a = 3 in (a - b) = -12, We get, b = 15

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