If $a$ and $b$ are the roots of the equation $y^2+y+1=0$,then the value of $a^4+b^4+a^{-1}b^{-1}$ is

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

Suppose $\alpha, \beta, \gamma$ are roots of $x^3+x^2+2x+3=0$. If $f(x)=0$ is a cubic polynomial equation whose roots are $\alpha+\beta, \beta+\gamma, \gamma+\alpha$,then $f(x)$ is equal to

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 $\alpha, \beta$ are the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ are the roots of $x^2 - 4x + q = 0$,and if $\alpha, \beta, \gamma, \delta$ are in a geometric progression,then the values of $p$ and $q$ are respectively:

If $\alpha, \beta, \gamma, \delta$ are the roots of $x^4 - 100x^3 + 2x^2 + 4x + 10 = 0$,then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} + \frac{1}{\delta}$ is equal to: