- #1

peripatein

- 880

- 0

## Homework Statement

I am expected to show that the polynomial

a

_{1}x

^{b1}+ a

_{2}x

^{b2}+ ... + a

_{n}x

^{bn}= 0

has at most n-1 solutions in (0,infinity), where a

_{1},a

_{2},...,a

_{n}are real numbers different than zero, and b

_{1},b

_{2},...,b

_{n}are real numbers so that b

_{j}is different than b

_{k}for j different than k.

## Homework Equations

## The Attempt at a Solution

I am trying to apply Rolle's theorem, but am not very successful at that. In general, between any two solutions the first derivative is equal to zero.

I first tried dividing by x

^{b1}noting that zero is not a solution and in order to obtain a simpler polynomial, but it is doubtful this is how it ought to be solved and it didn't seem to get me anywhere.

Would anyone kindly provide some further insight/guidance?