If α and β are the roots of the equation x² + px + 2 = 0 and 1/(α) and 1/(β) are the roots of the equation 2x² + 2qx + 1 = 0, then (α - 1/(α))(β - 1/(β))(α + 1/(β))(β + 1/(α)) is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2020 Mathematics question

JEE Main 2020 · 3 Sep, Morning shift · Q5144

JEE Main 20203 Sep, Morning shiftMathematicsHardComplex Numbers and Quadratic Equations264× since 2002

\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 :

JEE Main 2020 · 3 Sep, Morning shift · Q5144

JEE Main 20203 Sep, Morning shiftMathematicsHardComplex Numbers and Quadratic Equations264× since 2002

\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 :