Let $f\left(x\right)=\sin x+ax+b$, then $f\left(x\right)=0$ has :

Only one real root which is positive, if a<–1 & b<0

Only one real root which is negative, if a>1 & b> 0

Only one real root which is positive, if a>1 & b<0

Only one real root which is negative, if a<–1 & b<0