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WAEC Further Mathematics 2015 Question 19

Question 19

Polynomials

Given that x2 + 4x + k ≡ (x + r)2 + 1, find the values of k and r

  1. A.k = 5, r = −1
  2. B.k = 5, r = 2
  3. C.k = 2, r = 5
  4. D.k = 1, r = 5
Show the answer and explanation

Answer: B (k = 5, r = 2)

Explanation

(x + r)² + 1 = x² + 2rx + r² + 1, so 2r = 4 (r = 2) and k = 4 + 1 = 5.