$a,b\in R$,roots of $x^2+ax+b=0$ are $\alpha,\beta$ and roots of $x^2+bx+a=0$ are $\alpha+k,\beta+k$ where $k\neq 0$.$\alpha,\beta,k$ are real,a & b are positive,then

Question

$\begin{array}{1 1}(A)\;\text{Minimum value of a is 4}\\(B)\;\text{Minimum value of b is 4}\\(C)\;\text{No conclusion for values of a&b}\\(D)\;\text{None}\end{array}$