JEE 2023 — Mathematics PYQ

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