(a) Use the discriminant: . Since you want to show there are two real roots it must be greater than 0.
I'm not too sure about why you'd show it's greater than 0, hence the above is the best bet. I would assume that since the question says there are real roots it's fine to assume part a but meh,perhaps someone else knows more?
(b) Solve the equation given in part a for k using your favourite method