To elaborate on the result that nadeem and bsg used,

 

We know from the fundamental theorem of algebra state and factor theorem that the polynomial

 

P(x) = a_nxⁿ+a_n-1x^n-1+...+a_o has exactly n roots in the complex plane, say x₁, x₂, ..., x_n

 

So, we can write P(x) = a_n (x-x₁) (x-x₂)...(x-x_n)

 

Now, if this expression goes to zero for x_n+1 which is not equal to any of the other roots, then the only possibility is that a_n = 0.

 

This means P(x) = 0 for all x.