Consider the equation `x^4 + 2ax^3 + x^2 + 2ax + 1 = 0` where `a in R`. Also range of function `f(x)= x+1/x` is `(-oo,-2]uu[2,oo)` If equation has at least two distinct positive real roots then all possible values of a are

Options

A. 2
B. 1
C. 0
D. 3

Answer

3

Explanation

If exctly two roots are positive, the other two roots are negative. The -2 and 2 must lie between the roots. So,
`f(-2) lt 0 and f(2) lt 0`
`rArr a gt 3//4 and a gt lt - 3//4`
Hence, no such values of a exist.