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

Correct answer is D

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 \(\alpha\beta = \frac{n}{2} = 2 \implies n = 4\)