i) real coefficients - roots in conjugates
II) just factorise
ii) for there to be a real root, z-k=0 and kz-1=0 simultaneously. therefore, k = 1 or -1; sub this value in
iv) product of roots; modulus^4 = 1. and they all have equal modulus. therefore = 1
v) use sum of roots
vi) no idea
EDIT: with vi), i had an idea, but not enough time. sum of roots two at a time would give you a value of k^2. you would then use the fact that k=x-y to prove it is greater than something; and it should fall out somehow
i found it alright. there was too much conics and geometry imo and nowhere near enough mechanics. volumes by far hardest question. multiple choice was good but theres nowhere near enough structure with this change to multiple choice. last question wasnt too bad but 15a was challenging.