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If α and β are the roots of the equation \(...

If α and β are the roots of the equation 2x2+5x+n=0, such that αβ=2, find the value of n.

A.

-4

B.

-2

C.

2

D.

4

Correct answer is D

An equation can be written as x2(α+β)x+(αβ)=0

Making the coefficient of x2 = 1 in the given equation, we have

x2+52x+n2=0

Comparing, we have αβ=n2=2n=4