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.

I think more information is needed.

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1. There are two things you should never try to prove ...... the impossible and the obvious.

2. If you always do what you've always done, you'll always get what you've always got.

3. Lack of planning on your part does not constitute an emergency on my part.

4. Pressure makes diamonds.

This was all the information I was provided with . You mean there's no other way to find the zeroes of the quartic?

Thanks though. Your help was definitely appreciated.

Are you meant to get them in terms of a, b and c?

__________________
1. There are two things you should never try to prove ...... the impossible and the obvious.

2. If you always do what you've always done, you'll always get what you've always got.

3. Lack of planning on your part does not constitute an emergency on my part.

4. Pressure makes diamonds.

It doesn't state but I guess that's what you're supposed to do.