Cam someboy please help me out with this? I've done a part of it so far. This is the question:

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Given the polynomial has real coefficients.

IF we know has a complex zero (k being an integer), use this to find an expression for a real quadratic factor of .

Hence, find all the possible values for for which the quadratic is a factor of

Now, this is what I have done so far:

If is a zero, then is also a zero (conjugates).

From this, I used the sum and product rules:

SUM :

PRODUCT :

This gives

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What do I do with this? Now that I have a quadratic factor, I'm supposed to find the possible values of k. I was thinking maybe and that's the answer but I'm not sure (square rooting negative number gives an imaginary solution)

Can someone check it for me?

Thanks. All help is appreciated.