Wednesday, 2 October 2013

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

Suppose g(x)=a1x+a2x2+...+akxk and f(x)=bjxj where a1,a2...ak>0 , j{1,2.....,k1}, bj>0 and x0.



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!

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