- #1

Neoma

- 9

- 0

Suppose n is odd, prove that f has at least one and at most three real roots.

I thought about the intermediate value theorem for proving that f has one root, but then you need one x where f is negative and another one where it's positive and it's impossible to expres this x in terms of n, p and q.

To prove that f has at most three real roots, I thought about finding the local extrema (where f'(x)=0) and examining each of the possible combinations of positions of them. However, then I'm kinda facing the same problem. I'm sure there has to be some more elegant way.