Question

Let f (x) = sinx + ax + b. Then f(x) = 0 has

• A. only one real root which is positive if $a>1,b<0$
• B. only one real root which is negative if $a>1,b<0$
• C. only one real root which is negative if $a<-1,b>0$
• D. CAN'T SAY ANYTHING

Answer 1

The correct option is A only one real root which is positive if $a>1,b<0$

f'(x) = - cosx + a, if a $>$ 1,then f(x) entirely increasing. So f(x) =0 has only one real root, which is positive if f(0) $<$ 0 and negative if f(0) $>$ 0.

Similarly when a $<$ -1. Then f(x) entirely decreasing. So f(x) has only one real root which is negative if f(0) $<$ 0 and positive if f(0) $>$ 0