If one root of the equation $x^2 - 30x + p = 0$ is the square of the other root,then $p = \dots \dots \dots$

If $2, 3, 6$ are the roots of the polynomial $f(x) = x^3 + ax^2 + bx + c$,where $a, b, c \in \mathbb{C}$. Then,the value of $a - c$ is

If $\alpha, \beta, \gamma$ are the roots of $x^3+4x+1=0$,then the equation whose roots are $\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}, \frac{\gamma^2}{\alpha+\beta}$ is

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 - bx - c = 0$,then $\alpha^2 - \alpha\beta + \beta^2 = .......$

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

If the roots of the quadratic equation $x^2-35x+c=0$ are in the ratio $2:3$ and $c=6K$,then $K=$