SOLUTION: i and -2i are two zeros of {{{p(x)=x^6-2x^5+2x^4-10x^3-11x^2-8x-12}}}.
Find the other zeros and write p(x)as a product of linear factors.
Algebra.Com
Question 204277: i and -2i are two zeros of .
Find the other zeros and write p(x)as a product of linear factors.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Complex roots always come in conjugate pairs, so if 
is a root then so is 
. Likewise, if 
is a root, then so is 
. Therefore, four of the factors you are looking for are:
(x + i)(x - 2i)(x + 2i))
or
(x^2 + 4))
The next step is to do two iterations of polynomial long division using each of the two 2nd degree factors above. Polynomial long division is too difficult to render on this site -- at least I haven't figured out a way to actually show it in under 45 minutes to an hour of work. So I'm just going to give you the result and if you need to see those steps, you can either send a thank-you note reply with your request, or you can go to:
www.purplemath.com/modules/polydiv2.htm
Where you can see an excellent explanation of the process
Then
Which is then easily factored to:
(x + 1))
Therefore your six linear factors are:
(x + i)(x - 2i)(x + 2i)(x - 3)(x + 1))
John
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