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    Hey guys, been trying to figure out this question for a while and can't seem to get it. I've done the first part of the question, getting p = -8 and q = 9, and checking the answers that looks right.

    However I'm kinda stuck on part B now. The sum of roots I got was 3-7i by doing -b/a. I don't know if that's right and to be honest, I have no idea where to go from there.

    Can anybody give me a hint or some other way I could find the answer? Any help would be appreciated.

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    Sum of the roots is 3 + 7i, I'll assume you made a typo. If not, reply back.

    You're given that one root is 2 + 5i. If we call the other root z', then

    2+5i + z' = 3 + 7i... find z'...

    To answer the very last part, what do you notice about the coefficients of the quadratic?
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    I haven't checked your answer to part (a) so I'll assume it's correct.

    For part (b) you know that \alpha + \beta = 3+7i (where \alpha,\beta are the roots), but you know that one of the roots is equal to 2+5i, so \beta must be... [you do this bit].

    As for the reason why this isn't the complex conjugate, you should know this. Otherwise, think about when you would expect the roots to be conjugate. [All else failing, consult your textbook; that or someone will probably jump in and tell you anyway, but it's much more fun to find out for yourself.]
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    After looking at it again, I just realised why , sorry I was being a little slow. Thanks for your help guys :P
 
 
 
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