If $\alpha, \beta$ are the roots of the equation $x^2 + bx + c =0$ and $\alpha + h, \; \beta+h$ are the roots of the equation $x^2 + qx + r =0$, then $h$ is equal to :

Question

( A ) $\frac{1}{2} (b+q)$
( B ) $b-q$
( C ) $b+q$
( D ) $\frac{1}{2} (b-q)$