If $\alpha$ and $\beta$ are the roots of the equation $x^2 + ax + b = 0$,then the value of $\alpha^3 + \beta^3$ is equal to:

If $\alpha, \beta, 2 \beta$ are the real roots of the equation $x^3-9 x^2+k=0$ and $k \in R-\{0\}$,then $14 \beta=$

If one root of the quadratic equation $x^2 + px + q = 0$ is the square of the other,then:

If $x_1$ and $x_2$ are the real roots of the equation $x^2-kx+c=0$,then the distance between the points $A(x_1, 0)$ and $B(x_2, 0)$ is

Let $\alpha$ and $\beta$ be the roots of $x^2 - 6x - 2 = 0$,where $\alpha > \beta$. If $a_n = \alpha^n - \beta^n$ for all $n \geq 1$,then what is the value of $\frac{a_{10} - 2a_8}{2a_9}$?

If $\alpha$ and $\beta$ are the roots of $ax^2+bx+c=0$,then the roots of $ax^2-bx(x-1)+c(x-1)^2=0$ are