Vector Algebra: JEE Main 2023 Mathematics question

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