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WAEC Further Mathematics 2009 Question 9

Question 9

Polynomials

The roots of the quadratic equation 2x2 − 5x + m = 0 are α and β, where m is a constant. Find (α2 + β2) in terms of m.

  1. A.25/4 − m
  2. B.25/4 − 2m
  3. C.25/4 + m
  4. D.25/4 + 2m
Show the answer and explanation

Answer: A (25/4 − m)

Explanation

α + β = 5/2 and αβ = m/2. α2 + β2 = (α + β)2 − 2αβ = 25/4 − m.