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

If $$\alpha$$ and $$\beta$$ ($$\ne$$ 0) are the roots of the quadratic equation x² + $$\alpha$$x $$-$$ $$\beta$$ = 0, then the quadratic expression $$-$$x² + $$\alpha$$x + $$\beta$$, where x $$\in$$ R has

Let $$\alpha$$ and $$\beta$$ be real number and z be a complex number. If z² + $$\alpha$$z + $$\beta$$ = 0 has two distinct non-real roots with Re(z) = 1, then it is necessary that