The roots of the equation $x^2 + bx - c = 0$ where $b, c > 0$ are:

If the roots of the equation $ax^2 + bx + c = 0$ are real and of the form $\frac{\alpha}{\alpha - 1}$ and $\frac{\alpha + 1}{\alpha}$,then the value of $(a + b + c)^2$ is

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - 6x - 2 = 0$. If $a_n = \alpha^n - \beta^n$ for $n \ge 1$,then the value of $\frac{a_{10} - 2a_8}{2a_9}$ is equal to:

For the equation $3x^2 + px + 3 = 0, p > 0$,if one of the roots is the square of the other,then $p$ is equal to:

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3 - 3x^2 + x + 5 = 0$,then $y = \sum \alpha^2 + \alpha \beta \gamma$ satisfies which of the following equations?

The cubic equation whose roots are the squares of the roots of $x^3-2x^2+10x-8=0$ is