HMMT November 2009 U25

Find all solutions to $x^{4}+2 x^{3}+2 x^{2}+2 x+1=0$ (including non-real solutions).

Dataset text NuminaMath olympiads. Quoted with source.

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-1, i, -i

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.