Hello. I seem to be having a little trouble with this problem regarding quartics so if you could assist me, it would be greatly appreciated:

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A polynomial with real coefficients and two integer zeroes p and q is given as:



has a complex zeroes and

Using p and q, write another expression for a real quadratic factor of and using this, list the possible values of whereby , and are the zeroes of

So far, using sum and product, I wrote it as a quadratic factor:



That means the quartic can be written as (using the real and complex factor):



Is this right so far?

Given , show that there's only one possible value for and hence, find all the zeroes of

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If you could help me out here, it would be greatly appreciated.

Thank you.