You do understand that this is not a homework service nor is it a tutorial service. PLease either post some of your own work on this problem or explain what you do not understand about the question.
The thing I'm not sure about is whether there are any other real values of k apart from k=14 that would give at least one repeated root...
I'm not sure what you are trying to do here. You seem to be assuming that x must be an integer, which is not true. If x= a, say, is a repeated root then there is a factor of . Try writing .