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

If $$\mathrm{P}(x)=\mathrm{a} x^2+\mathrm{b} x+\mathrm{c}$$ and $$\mathrm{Q}(x)=-\mathrm{a} x^2+\mathrm{d} x+\mathrm{c}$$ where $$\mathrm{ac} \neq 0$$, then $$\mathrm{P}(x) \cdot \mathrm{Q}(x)=0$$ has (a, b, c, d are real)