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 :

Let f(x) be a quadratic polynomial such that
f(–1) + f(2) = 0. If one of the roots of f(x) = 0
is 3, then its other root lies in :

Let $$\alpha $$ and $$\beta $$ be the roots of the equation
5x² + 6x – 2 = 0. If S_n = $$\alpha $$ⁿ + $$\beta $$ⁿ, n = 1, 2, 3...., then :

Let a, b $$ \in $$ R, a $$ \ne $$ 0 be such that the equation, ax² – 2bx + 5 = 0 has a repeated root $$\alpha $$, which is also a root of the equation, x² – 2bx – 10 = 0. If $$\beta $$ is the other root of this equation, then $$\alpha $$² + $$\beta $$² is equal to :