Question

If the equation `a sin^(3)x+(b-s)sin^(2)x+(c-b)sin x=c =0` has exactly three distinct solutions in `[0, pi]`, where a + b + c = 0, then which of the following is not the possible value of c/a ?
A. 1
B. `(1)/(4)`
C. `(sqrt(2))/(7)`
D. `(2)/(7)`

Answer 1

Correct Answer - A
`a sin^(3)x + (b-a)sin^(2)x + (c-b)sin x-c=0`
`rArr (sin x-1)(a sin^(2)x + b sin x + c)=0`
Also a + b + c = 0
`therefore` one of the solutions of the equation `a sin^(2) x + b sin x + c = 0`
is sin x = 1
Product of roots = x/a ltbRgt For three solutions, we must have `0 le (c )/(a) lt 1`