An arc \( PQ \) of a circle subtends a right angle at its centre \( O \). The midpoint of the arc \( PQ \) is \( R \). If \(\overrightarrow{ OP} =\vec{u} \), \(\overrightarrow{ OR} = \vec{v} \) and \(\overrightarrow{ OQ} = \ {\alpha \vec{u}} + \beta \vec{v} \), then \( \alpha, \ \beta^2 \) are the roots of equation.
