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WAEC Further Mathematics 2006 Question 12

Question 12

Polynomials

The roots of the equation 2x2 + kx + 5 = 0 are α and β, where k is a constant. If α2 + β2 = −1, find the values of k.

  1. A.±16
  2. B.±8
  3. C.±4
  4. D.±2
Show the answer and explanation

Answer: C (±4)

Explanation

α + β = −k/2 and αβ = 5/2. α² + β² = (α + β)² − 2αβ = k²/4 − 5 = −1, so k² = 16 and k = ±4.