Quadratics positive for every real input

(a) Show that if $x^2>k(x+1)$ for all real $x$, then $-4<k<0$.

(b) Find the range of values of $k$ for which $x^2+2kx+15-2k$ is always positive for all real $x$. Deduce the range of values of $k$ for which $k(x^2+2kx+15-2k)>0$ for all real $x$.