The roots of a cubic equation $f(x)=0$ are diminished by $\frac{-3}{2}$ so, as to remove the term containing $x^2$ and the transformed equation is $8 x^3-54 x-78=0$. Then, the equation $f(x)=0$ is

If $\alpha$ and $\beta$ are the roots of a quadratic equation $x^2+b x+c=0$ such that $\alpha^2+\beta^2=5$ and $\alpha^3+\beta^3=9$, then $b+c=$

The set of all real values of the expression $\frac{x^2-x+2}{x^2+x-2} \forall x \in R-\{-2,1\}$ is

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3-9 x^2+23 x-15=0$, then $\alpha^3+\beta^3+\gamma^3=$