I could use some input on this one: Let n be an integer greater than 1.

Which of the following conditions guarantee that the equation $\displaystyle x^n=\sum _{i=0}^{n-1}a_ix^i$ has at least one root in the interval (0,1)?

I. $\displaystyle a_0>0\ \& \sum _{i=0}^{n-1}a_i<1$

II. $\displaystyle a_0>0\ \& \sum _{i=0}^{n-1}a_i>1$

III. $\displaystyle a_0<0\ \& \sum _{i=0}^{n-1}a_i>1$