If one root of $5x^2 + 13x + k = 0$ is the reciprocal of the other,then $k = $?

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

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + px + q = 0$,then what is the equation whose roots are $q/\alpha$ and $q/\beta$?

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2 - \lambda)x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is

If the sum of two roots of the equation $x^4+2x^3-7x^2-8x+12=0$ is zero,then the sum of the squares of the other two roots is

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 35x + 2 = 0$,then the value of $(2\alpha - 35)^3 \cdot (2\beta - 35)^3$ is equal to