should that be "equal roots"?

if so, then

you need the discriminant to be zeroA) Find the possible values of k

B) Solve f(x) = 0 for each possible value of k

this is asking you to complete the square, do you know how to do that? (you can google it )Given instead that k = 8

C) Express f(x) in the form (x + a)squared + b, where a and b are constants.

use the quadratic formula. do you remember it?D) Solve f(x) = 0 giving your answers in surd form