Solve the following equation in the complex number system.
x^(5)+6x^(3)-8x(2)-48=0

Question

Solve the following equation in the complex number system. 
x^(5)+6x^(3)-8x(2)-48=0

anonymous · Answer

by some miracle this factors as 
$$(x^2+6) (x^3-8) = 0$$

jamesj · Answer

So you see by inspection that x = 2 is a root ... and sat73 has given most of this to you now ...

anonymous · Answer

solution for first factor is straight forward. write 
$$x^2+6=0,x^2=-6,x=\pm\sqrt{6}i$$

jamesj · Answer

Now I think you should find the other roots by yrself! ;-)

anonymous · Answer

for second factor jamesj said one solution is 0, so you can factor as the difference of two cubes to get 
$$(x-2)(x^2+4x+4)$$ and now quadratic formula for second part
i will keep quiet

jamesj · Answer

" jamesj said one solution is 2", yep.

anonymous · Answer

yes of course i meant one solution is x = 2, not x = 0 !

anonymous · Answer

typo its 8x^(2)

anonymous · Answer

both jamesj and i knew you meant 
$$8x^2$$
the solution is right