An arc PQ of a circle subtends a right angle at its centre O. The… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 10 April, Shift 1Circle Equation & Properties

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

A
$3x^2-2x-1=0$
B
$3x^2+2x-1=0$
C
$x^2-x-2=0$
D
$x^2+x-2=0$

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