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JAMB Mathematics 1987 Question 21

Question 21

Quadratic Equations

Find the values of m which make the following quadratic function a perfect square.
x2 + 2(m + 1)x + m + 3

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

Answer: C (1, −2)

Explanation

A perfect square needs (half the x-coefficient)² = constant: (m + 1)² = m + 3. This gives m² + m − 2 = 0, so (m + 2)(m − 1) = 0 and m = 1 or −2.