If $6 x-x^2+12$ attains its extreme value $\beta$ at $x=\alpha$, then $\beta=$

Let $a$ be a common root of the equations $x^3-2 x-25 \lambda=0,3 x^3-8 x-\frac{175}{3} \lambda=0$ and $\lambda>0$. Then, $\lambda=$

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

If $\alpha$ and $\beta$ are the irrational roots of the equation $3 p^2 x^3+p x^2+q x+3=0$ when $p=1$ and $q=-7$, then $|\alpha-\beta|=$