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JAMB Mathematics 1984 Question 26

Question 26

Polynomials

If (x − 2) and (x + 1) are factors of the expression x3 + px2 + qx + 1, what is the sum of p and q?

  1. A.0
  2. B.−3
  3. C.3
  4. D.−17/3
  5. E.−2/3
Show the answer and explanation

Answer: B (−3)

Explanation

x = 2: 8 + 4p + 2q + 1 = 0. x = −1: −1 + p − q + 1 = 0, so p = q. Then 6p = −9, p = q = −3/2 and p + q = −3.