Let `f(x)=sinx+a x+bdot` Then which of the following is/are true? (a) `f(x)=0` has only one real root which is positive if `a >1, b<0.` (b)`f(x)=0` has only one real root which is negative if `a >1, b<0.` (c)`f(x)=0` has only one real root which is negative if `a >1, b > 0.` (d) none of these

Options

A. f(x) =0 has only one real root which is positive if `gt1, blt0`
B. f(x) =0 has only one real root which is negative if `agt1,bgt0`
C. f(x) =0 has only one real root which is negative if `alt-1 , blt0`
D. None of these

Answer

1,2,3

Explanation

f(x)=cosx +a

If `agt1` then `f(X) gt0` or f(x) is an increasing funciton .Then
f(x) =0 has +ve root if b `lt` 0 and -ve root if b `gt` 0
f(X)=cos x+a
If a `lt`-1 then f(X) `lt` 0 or f(X) is a decreasing function then
f(x) =0 has negative root if b `lt` 0