<s>[INST] Find the roots of the summed polynomial 
Find the roots of: $$x^7 + x^5 + x^4 + x^3 + x^2 + 1 = 0$$

I got that:
$$\frac{1 - x^8}{1-x} - x^6 - x = 0$$
But that doesnt make it any easier.
 [/INST] Clever factoring: $x^7+x^5+x^4+x^3+x^2+1 =(x+1)(x^2 - x + 1)(x^4+x^2+1)$
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