If $\alpha$ and $\beta$ are the roots of the equation $x^2+4x+12=0$ such that $\alpha-\beta=1$,then the value of $k$ is _______

Question

$\begin{array}{1 1}(A) \;k=7\\(B)\;k=-7\\(C)\;k=\frac{15}{2}\\(D)\;\text{None of the above}\end{array}$