If (alpha) and (beta) are the roots of the equation (2x^{2} + 5x + n = 0), such that (alphabeta = 2), find the value of n.
-
A.
-4 -
B.
-2 -
C.
2 -
D.
4
Correct Answer: Option D
Explanation
An equation can be written as (x^{2} – (alpha + beta)x + (alphabeta) = 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 (alphabeta = frac{n}{2} = 2 implies n = 4)