Hi there,
I have to answer to following question, and am having issues:
Given that is a root of the polynomial equation
,
find all other roots.
I can see that is a root, and that because of conjugate pairs, must be, and I understand that there must be 6 roots due to the degree of the polynomial, but I don't know how to find the other 3. Any advice or pointers would be hugely appreciated!
Thanks in advance!
Ok, getting there, and thanks for picking up my mistake in typing above. I am still having a slight issue though;
I have taken the 4 roots,
, , and ,
and multiplied them together as follows,
,
giving the following polynomial,
.
I have divided this by the original polynomial,
,
but each time I get the same thing,
remainder ,
which clearly isn't correct.
Am I doing something wrong in thr division of polynomials, or have I perhaps multiplied the roots together incorrectly? I've reached the point where I have retried the problem on so many occasions I cant work out what's going wrong.
Any help much appreciated!