why friction is not needed to maintain optimum speed on a banked road

Dear student

If the road is flat the centripetal force is provided by the friction between the road and tires of vehicle.
So if there is no friction, there has to be some force that can provide that necessary centripetal force and it is provided by making the road banked. The normal force on the vehicle now is not perpendicular to the ground so it can be split into vertical component and horizontal component. The horizontal component is provide the centripetal force to the vehicle. Mathematically 
$$\begin{gathered} N\sin \theta =\frac{m{v}^2}{r} and \\ N\cos \theta =mg \\ \Rightarrow \frac{m{v}^2}{r}=mg\tan \theta \\ \Rightarrow v=\sqrt{rg\tan \theta } \end{gathered}$$
This provide the velocity in the absence of friction.