If `alpha, beta` are roots of the equation `ax^(2) + 3x + 2 = 0 (a lt 0), "then"(alpha^(2))/(beta)+(beta^(2))/(alpha)` is greater than

Options

A. 0
B. 1
C. 2
D. none of these

Answer

D

Explanation

Since a `lt` 0, therefore discriminant `D = 9 - 8a gt 0`.
So, `alpha and beta` are real.
We have, `alpha+beta=-(3)/(a) and alpha beta=(2)/(a)`
`therefore" "(alpha^(2))/(beta)+(beta^(2))/(alpha) = (alpha^(3)+beta^(3))/(alpha beta)=((alpha+beta)^(3) - 3alpha(alpha+beta))/(alpha beta)`
`rArr" "(alpha^(2))/(beta) + (beta^(2))/(alpha)=((alpha+beta)^(3))/(alpha beta) - 3 (alpha+beta) = -(27)/(2a^(2))+(9)/(a) lt 0" "[because a lt 0]`