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

If one root of the equation $x^3-9x^2+26x-24=0$ is twice the other,then the sum of the cubes of those two roots is

If $\alpha_1, \alpha_2, \alpha_3, \alpha_4, \alpha_5$ are the roots of $x^5-5 x^4+9 x^3-9 x^2+5 x-1=0$,then $\frac{1}{\alpha_1^2}+\frac{1}{\alpha_2^2}+\frac{1}{\alpha_3^2}+\frac{1}{\alpha_4^2}+\frac{1}{\alpha_5^2}=$

The minimum value of the sum of the squares of the roots of $x^{2}+(3-a)x+1=2a$ is:

If $\alpha$ and $\beta$ are the roots of $x^2-2x+4=0$,then the value of $\alpha^6+\beta^6$ 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: