p294 q16 c

given

.......(*), where k is real, has no real roots.

find , in terms of k, the squares of the roots of (*), expressing the answers in the form x+iy where x and real are real.

as k varies, find the equation of the locus of the pts in the argand plane representing the squares of the roots of (*)

my working:

square of the roots

don't know how to find the locus. thanks.