$\alpha, \beta$ and $\gamma$ are the roots of the equation $8 x^3-42 x^2+63 x-27=0$. If $\beta<\gamma<\alpha$ and $\beta, \gamma$ and $\alpha$ are in geometric progression, then the extreme value of the expression $\gamma x^2+4 \beta x+\alpha$ is

If $\frac{2 x^3+1}{2 x^2-x-6}=a x+b+\frac{A}{P x-2}+\frac{B}{2 x+q}$, then 51 apB $=$

$\alpha$ is a root of the equation $\frac{x-1}{\sqrt{2 x^2-5 x+2}}=\frac{41}{60}$. If $-\frac{1}{2}<\alpha<0$, then $\alpha$ is equal to

$\alpha, \beta, \gamma, 2$ and $\varepsilon$ are the roots of the equation

$$ \begin{aligned} & \alpha, \beta, \gamma+4 x^4-13 x^3-52 x^2+36 x+144=0 . \text { If } \\ & \alpha<\beta<\gamma<2<\varepsilon \text {, then } \alpha+2 \beta+3 \gamma+5 \varepsilon= \end{aligned} $$