the first part is straightforward. for the roots i get .
For the quadratic I guessed got the root as the complex conjugate which is
i get that
and B is the product of the roots, but I am having trouble showing the required results.
If is a root then , i.e. conjugate is a root. Note, , thus, . But since . Thus, . This immediately implies, and . Thus, is the other root.
This means (by Viete) that . Because we are using the fact that the sum of the roots of unity is zero, i.e. .
Now the product is, . Here we would the fact that . Thus, we have that .
This means that: and solve .
Now, are its solutions. Thus, they are actually (not necessarily in that order).
This means, .
You need to determine the sign. That is what the problem says.