If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-5x^2-2x+24=0$,then $\frac{\beta\gamma}{\alpha}+\frac{\gamma\alpha}{\beta}+\frac{\alpha\beta}{\gamma}=$

For the equation $ax^2 + bx + c = 0$,the roots are $\alpha, \beta$,and for the equation $Ax^2 + Bx + C = 0$,the roots are $\alpha - k, \beta - k$. Then $\frac{B^2 - 4AC}{b^2 - 4ac} = \dots$

If $\alpha, \beta$ are the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ are the roots of $x^2 - 4x + q = 0$,and if $\alpha, \beta, \gamma, \delta$ are in a geometric progression,then the values of $p$ and $q$ are respectively:

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^{2} + \lambda x - 1 = 0$ is $15$,then $6(\alpha^{3} + \beta^{3})^{2}$ is equal to