# Complex roots of a 7th degree polynomial

Algebra Level 5

Consider the equation:

$x^7+x^6+x^5+x^4+x^3+x^2+x+1=0$

Let $$x_k$$ be the $$k^\text{th}$$ distinct root of the equation, and let $$\Re(x_k)$$ be the real part of that root.

$\sum_{k=1}^7{\left[\Re(x_k)\right]^2}=\ ?$

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