If the product of the roots of the equation $(a + 1)x^2 + (2a + 3)x + (3a + 4) = 0$ is $2$,then the sum of the roots will be:

If $\alpha, \beta$ are the roots of the equation $x^2 + px + 1 = 0$ and $\gamma, \delta$ are the roots of the equation $x^2 + qx + 1 = 0$,then $q^2 - p^2 = \dots$

If $\alpha, \beta$ are the roots of the equation $Ax^2 + Bx + C = 0$ and $\alpha^2, \beta^2$ are the roots of the equation $x^2 + px + q = 0$,then $p = \dots$

If $\alpha, \beta$ are the roots of the equation $x^2+3x+k=0$ and $\alpha+\frac{1}{\alpha}, \beta+\frac{1}{\beta}$ are the roots of the equation $4x^2+px+18=0$,then $k$ satisfies the equation:

If $\alpha$ and $\beta$,$\alpha$ and $\gamma$,$\alpha$ and $\delta$ are the roots of the equations $ax^2 + 2bx + c = 0$,$2bx^2 + cx + a = 0$ and $cx^2 + ax + 2b = 0$ respectively,where $a, b$ and $c$ are positive real numbers,then $\alpha + \alpha^2 = $

The value of $p$ for which the sum of the squares of the roots of the equation $x^2 - (p + 3)x + (5p - 2) = 0$ assumes its least value is: