If cot $$\alpha$$ and cot $$\beta$$ are the roots of the equation x² + bx + c = 0 with b $$\ne$$ 0, then the value of cot ($$\alpha$$ + $$\beta$$) is

The sum of the roots of the equation x² + bx + c = 0 (where, b and c are non-zero) is equal to the sum of the reciprocals of their squares. Then, $${1 \over c},b,{c \over b}$$ are in

The sum of the roots of the equation ax² + x + c = 0 (where, a and c are non-zero) is equal to the sum of the reciprocals of their squares. Then, a, ca², c² are in

If S = {x : x² + 1 = 0, x is real}, then S is