Question 231979
{{{x^6 + 9x^3 + 8 = 0}}}
I took a direct approach and factored it into
{{{(x^3 + 8)(x^3 + 1) = 0}}}
{{{x^3 = -8}}} is a solution
{{{x = -2}}}
I need the other 2 roots now. I proceed to cheat and
apply what I know about complex roots, namely that 
they are equally spaced aound the complex plane. That means
the 3 roots are 120 degrees apart. One complex root is
30 degrees from the vertical in 1st quadrant, the other is
30 degrees from vertical in 4th quadrant. The components of
the complex roots are 
{{{x = 1 + sqrt(3)i}}} (1st quadrant) and
{{{x = 1 - sqrt(3)i}}} (4th quadrant).
I do the same for {{{x^3 + 1}}}
{{{x^3 = -1}}}
The complex roots are 
{{{x = 1/2 + (sqrt(3)/2)*i}}} (1st quadrant) and
{{{x = 1/2 - (sqrt(3)/2)*i}}} (4th quadrant
I don't know an easy way to prove that's right, but
I'm pretty sure it is