If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-9x^2+23x-15=0$,then $\alpha^3+\beta^3+\gamma^3=$

The cubic equation whose roots are the squares of the roots of the equation $12x^3-20x^2+x+3=0$ is

If the roots of the given equation $(2k + 1)x^2 - (7k + 3)x + k + 2 = 0$ are reciprocal to each other,then the value of $k$ will be

If $\alpha, \beta, \gamma$ are the roots of $x^3+ax^2+bx+c=0$,then find the value of $\sum \frac{1}{\alpha}$,given that $\alpha, \beta, \gamma$ are non-zero.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + \frac{a}{2} x + b = 0$ and $(\alpha-\beta)(\alpha-\gamma)$,$(\beta-\alpha)(\beta-\gamma)$,$(\gamma-\alpha)(\gamma-\beta)$ are the roots of the equation $(y+a)^3 + K(y+a)^2 + L = 0$,then $\frac{L}{K} =$

If the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ differ by the same quantity,then $b + c$ is equal to