If sin $$\theta$$ and cos $$\theta$$ are the roots of equation ax² $$-$$ bx + c = 0, then a, b and c satisfy the relation

Let a, b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax² + bx + c = 0

If the ratio of the roots of the equation $$p{x^2} + qx + r = 0$$ is $$a:b$$, then $${{ab} \over {{{(a + b)}^2}}}$$ =

If $$\alpha$$ and $$\beta$$ are the roots of the equation x² + x + 1 = 0, then the equation whose roots ar $$\alpha$$¹⁹ and $$\beta$$⁷ is