The function is .

Apply derivative on each side with respect to .

The derivative function is always positive, since  and  is any positive integer.

The only way a function  have a positive derivative for  is function to be monotonically increasing.

A monotonically increasing function can cross the  axis at most once.

Therefore  has a atleast one real root.

The other roots must be complex.

Therefore the polynomial function  cannot have two real roots.

The polynomial function  cannot have two real roots.