(i) The sign given to the focal length of a concave mirror (according to the New Cartesian Sign Convention) is negative. This is because the focus of a concave mirror is in front of the mirror, on the left side.
(ii) The sign given to the focal length of a convex mirror (according to the New Cartesian Sign Convention) is positive. The is because the focus of a convex mirror is behind the mirror, on the right side.