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

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

If $f(x)=ax^2+bx+c$ satisfies $f(1)+2f(2)=0$ and $2f(1)+f(2)=0$,then $3a+b=$

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

If the difference between the roots of the equation $(k - 2)x^2 - (k - 4)x - 2 = 0$ is $3$, find the value of $k$.

Suppose $\alpha, \beta, \gamma$ are the roots of $x^3+x^2+x+2=0$. Then,the value of $\left(\frac{\alpha+\beta-2 \gamma}{\gamma}\right)\left(\frac{\beta+\gamma-2 \alpha}{\alpha}\right)\left(\frac{\gamma+\alpha-2 \beta}{\beta}\right)$ is