Polynomials question

[Tofu]

I'm struggling with b, c, and d of this question. I have the answer but don't know the method. I've attached the question and the answer, so can somebody please explain to me how you get to the answer?

 

[Cubist]

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You didn't show your thoughts, or you might have had a response by now. Here''s a hint:- using the result of part a) we have...

(x - p) * (x - q) * (x² - 2x + (1 + k²)) = x⁴ + ax³ + bx² + cx - 10

Combine this with the constraints on p,q and k. Can you think of a method that can be used to find the possible values of k?

 

[Dr.Peterson]

I'm struggling with b, c, and d of this question. I have the answer but don't know the method. I've attached the question and the answer, so can somebody please explain to me how you get to the answer?View attachment 29155View attachment 29156

Of course, the given answer to (b) is wrong ...

I don't suppose that's what you're concerned about.

But I'll add a hint: Focus on the constant term in P(x).