If $\alpha $ and $\beta $ are the roots of the equation x2 + px + 2 = 0 and ${1 \over \alpha }$ and ${1 \over \beta }$ are the roots of the equation 2x2 + 2qx + 1 = 0, then $\left( {\alpha - {1 \over \alpha }} \right)\left( {\beta - {1 \over \beta }} \right)\left( {\alpha + {1 \over \beta }} \right)\left( {\beta + {1 \over \alpha }} \right)$ is equal to :

Question

If $\alpha $ and $\beta $ are the roots of the equation
x² + px + 2 = 0 and ${1 \over \alpha }$ and ${1 \over \beta }$ are the
roots of the equation 2x² + 2qx + 1 = 0, then
$\left( {\alpha - {1 \over \alpha }} \right)\left( {\beta - {1 \over \beta }} \right)\left( {\alpha + {1 \over \beta }} \right)\left( {\beta + {1 \over \alpha }} \right)$ is equal to :

${9 \over 4}\left( {9 - {q^2}} \right)$

${9 \over 4}\left( {9 + {q^2}} \right)$

${9 \over 4}\left( {9 - {p^2}} \right)$

${9 \over 4}\left( {9 + {p^2}} \right)$

Solution

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