If $\alpha$ is the positive root of the equation, $p ( x ) = x ^ { 2 } - x - 2 = 0$, then $\lim _ { x \rightarrow \alpha ^ { + } } \frac { \sqrt { 1 - \cos p ( x ) } } { x + \alpha - 4 }$ is equal to\\
(1) $\frac { 3 } { 2 }$\\
(2) $\frac { 3 } { \sqrt { 2 } }$\\
(3) $\frac { 1 } { \sqrt { 2 } }$\\
(4) $\frac { 1 } { 2 }$