How Do You Solve x^4 + 2x^2 + x + 2 = 0?

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OK, problem with this equation:

x^4 + 2x^2 + x + 2 = 0

What is/are the solution(s)? I can't figure out how to factor this so that I can find the zeros or whatever...
 
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Hint: It has no Real zeros.
 
it is possible to factor it over the integers.

suppose you have a polynomial P of degree p. you want to factor it as P = Q R where Q and R are polynomials. consider the different degrees Q and R might have if p = 4 as in your case. this consideration will direct the trials and errors when looking for Q and R.
 
How can I prove that I have no zeros?
 
that'll be clear once you factor it.
 

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