real analysis - How many times can these two polynomial intersect with each other?

Suppose $g(x)=a_1x+a_2x^2+...+a_kx^k$ and $f(x)=b_jx^j$ where $a_1,a_2...a_k>0$ , $j\in \{1,2.....,k-1\}$, $b_j >0$ and $x\geq0$.

Intuitively, I think they can have at most two intersections. Is that correct?

Well, the answer is it has two positive roots by Descartes' rule of signs. Thanks for your help!