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.