If $\alpha, \beta, \gamma$ are the roots of $x^3+2x+5=0$,then $\sum \frac{\beta+\gamma}{\alpha^2} = $

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is $2$. Then the roots of the equation are:

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 - bx - c = 0$,then $\alpha^2 - \alpha\beta + \beta^2 = .......$

If $\sin 2 \theta$ and $\cos 2 \theta$ are solutions of $x^2+bx-c=0$,then

If the roots of the equation $(x - a)(x - b) = c$ (where $c \neq 0$) are $\alpha$ and $\beta$,then what are the roots of the equation $(x - \alpha)(x - \beta) + c = 0$?

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 $\frac{1}{\alpha_1^2}+\frac{1}{\alpha_2^2}+\frac{1}{\alpha_3^2}+\frac{1}{\alpha_4^2}+\frac{1}{\alpha_5^2}=$