Step-by-step Solution:

Suppose \(\mathrm{f}(\mathrm{x})=3 x^{5}+15 x-8\) Number of sign changes in \(f(x)=0\) is only 1 , hence there can be maximum one positive root of \(f(x)=0\). \[\] Number of sign changes in \(f(-x)=0\) is none. Thus there is no negative root. But degree of equation is 5 , therefore, there is at least one real root. So there must be one real positive root.\[\]Choice (C)\[\]