For the equation $x^4+x^3-4x^2+x-1=0$,the ratio of the sum of the squares of all the roots to the product of the distinct roots is

Let $A = \left| \begin{matrix} 2 & e^{i \pi} \\ -1 & i^{2012} \end{matrix} \right|$,$C = \left. \frac{d}{dx} \left( \frac{1}{x} \right) \right|_{x=1}$,and $D = \int_{e^2}^{1} \frac{dx}{x}$. If the sum of two roots of the equation $Ax^3 + Bx^2 + Cx - D = 0$ is equal to zero,then $B$ is equal to:

If $2$ and $3$ are two roots of the equation $2x^3 + mx^2 - 13x + n = 0$,then the values of $m$ and $n$ are respectively

If $\alpha, \beta, \gamma$ are the roots of $2x^3 - 2x - 1 = 0$,then $(\Sigma \alpha \beta)^2$ is equal to

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x+6=0$,then $\Sigma \alpha^2 \beta+\Sigma \alpha \beta^2$ is equal to :

If the sum of the squares of the roots of the equation $x^2-(a-2)x-(a+1)=0$ is least for an appropriate value of the variable parameter $a$, then the value of $a$ will be