If equation `(cos^(-1)x)^(4)-8(cos^(-1)x)^(3) + a (cos^(-1)x)^(2)+b (cos^(-1)x)+16=0` has four positive real roots, where a, b epsilon R then `[x]` = (Where [.] G.I.F.)

Options

A. `1`
B. `0`
C. `-1`
D. `2`

Answer

C

Explanation

All th roots of given equation are equal therefore
`cos^(-1) x=2`
`therefore x = cos 2`
`[x]=[cos 2] =-1`