There is this identity
=
which is valid for any real or complex number z.
(This formula is the same as the formula for the sum of first 5 terms of a geometric progression).
So, if z is the root of the equation = 0 (any of five complex roots), then
= 0. (1)
Thus in our case
= 0, (2)
where r is the complex root of with smallest positive argument.
Since in our case the factor r+1 is not zero (because r =/= -1).
we can divide both sides of (2) by (r+1).
We will get then
= 0.
It implies that
= 0. ANSWER