If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$,then the equation whose roots are $\alpha+\beta$ and $\frac{1}{\alpha}+\frac{1}{\beta}$ is

If $\alpha, \beta$ are the roots of $ax^2 + bx + c = 0$ and $\gamma, \delta$ are the roots of $px^2 + qx + r = 0$,and $D_1, D_2$ are their respective discriminants. If $\alpha, \beta, \gamma, \delta$ are in arithmetic progression,then $D_1 : D_2 = \dots$

If $a, -a, b$ are the roots of $x^{3}-5x^{2}-x+5=0$,then $b$ is a root of

If $\alpha, \beta, \gamma$ are roots of the equation $x^3+a x^2+b x+c=0$,then $\alpha^{-1}+\beta^{-1}+\gamma^{-1} = $

If $x_1$ and $x_2$ are the real roots of the equation $x^2-kx+c=0$,then the distance between the points $A(x_1, 0)$ and $B(x_2, 0)$ is

The $G.M.$ of the roots of the equation $x^2 - 18x + 9 = 0$ is