If $\alpha$ and $\beta$ are the roots of $x^2-10x-8=0$ with $\alpha > \beta$,and $a_n = \alpha^n - \beta^n$ for $n \in N$,then the value of $\frac{a_{10}-8a_8}{5a_9}$ is:

If $\alpha$ and $\beta$ are roots of the equation $x^{2}+x+1=0$,then $\alpha^{2}+\beta^{2}$ is

If the difference between the roots of the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then:

Let $\alpha, \beta, \gamma$ be the roots of $x^3+x+10=0$ and $\alpha_1=\frac{\alpha+\beta}{\gamma^2}, \beta_1=\frac{\beta+\gamma}{\alpha^2}, \gamma_1=\frac{\gamma+\alpha}{\beta^2}$. Then,the value of $(\alpha_1^3+\beta_1^3+\gamma_1^3)-\frac{1}{10}(\alpha_1^2+\beta_1^2+\gamma_1^2)$ is

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of the reciprocals of their squares,then $bc^2, ca^2, ab^2$ will be in

If $\alpha, \beta, \gamma$ are the roots of the equation $5x^3 - 3x^2 + 2x - 4 = 0$,then find the value of $\sum \alpha^2 \beta^2$.