if `x^(4)+3cos(ax^(2)+bx+c)=2(x^(2)-2)` has two solution with a,b,c `in` (2,5) then value of `(ac)/(b^(2))` can not be

Options

A. 4
B. 2
C. 1
D. 3

Answer

A, B, C

Explanation

Solution exist when `LHS=RHS=0`
`impliesx=+-1` and `cos(ax^(2)+bx+x)=-1`
When `x=1` `impliescos(a+b+c)=-1`
and when `x=-1impliescos(a-b-c)=-1`
As a,b,c `in(2,5),a+b+cin(6,15)` and
`(a-b-c)in(-1,8)`
`a+b+c=3pi` and `a-b+c=pi`
`AMgeGM,(a+c)/(2)gtsqrt(ac)impliesaclepi^(2)`