# Something having to do with roots and i and stuff

Algebra Level 5

$\large[(x-1)^2+4x][(x-1)^2+x][(x-1)^2+2x]=8x^3$

Suppose $$a_i$$ where $$i={{1,2,3,4,5,6}}$$ are the 6 complex roots of the equation above.

And $$\arg(x_j)\leq \arg(x_k)$$ for $$j\leq k$$.

In which quadrant does $$x_1x_6$$ lie in?

Details and Assumptions:

• $$0\leq \arg(x_i)<2\pi$$

• You may want to use a calculator at the end after you had found the exact values of the roots.

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