If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x + n = 0\), such that \(\alpha\beta = 2\), find the value of n.

  • A -4
  • B -2
  • C 2
  • D 4
waec 2018furthermathematics

The correct answer is D. 4

An equation can be written as \(x^{2} - (\alpha + \beta)x + (\alpha\beta) = 0\)

Making the coefficient of \(x^{2}\) = 1 in the given equation, we have

\(x^{2} + \frac{5}{2}x + \frac{n}{2} = 0\)

Comparing, we have \(\alpha\beta = \frac{n}{2} = 2 \implies n = 4\)

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