Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

" jamesj said one solution is 2", yep.

Answer 7

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

Answer 8

typo its 8x^(2)

Answer 9

both jamesj and i knew you meant
\[8x^2\]
the solution is right