For what value of $m$ will one root of $x^2 - 3x + 2m = 0$ be double one root of $x^2 - x + m = 0$?

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 sum of two roots of the equation $x^3-7px^2+5qx-6r=0$ is zero,then

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 $\frac{L}{K} =$

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

If the difference between the roots of the equation $x^2 - px + 8 = 0$ is $2$,then $p = ......$