Let $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sinx}+\mathrm{ax}+\mathrm{b},$ then which of the following is/are true? 

f(x) = 0 has only one real root which is positive if $\mathrm{a}>1,\mathrm{b}<0$

f(x) = 0 has only one real root which is negative if $\mathrm{a}>1,\mathrm{b}>0$

f(x) = 0 has only one real root which is negative if $\mathrm{a}<-1,\mathrm{b}<0$

f(x) = 0 has only one real root which is positive if $\mathrm{a}<-1,\mathrm{b}<0$