If the roots of the equation $x^2 + px + q = 0$ are $p$ and $q$,then what must be the value of $p$?

If $\alpha, \beta$ are the roots of $ax^2 + bx + c = 0$ and $\gamma, \delta$ are the roots of $px^2 + qx + r = 0$,and $D_1, D_2$ are their respective discriminants. If $\alpha, \beta, \gamma, \delta$ are in arithmetic progression,then $D_1 : D_2 = \dots$

If the product of the roots of the equation $2x^2 + 6x + \alpha^2 + 1 = 0$ is $-\alpha$,then the value of $\alpha$ will be

If the roots of the equation $ax^2 + bx + c = 0$ are $l$ and $2l$,then

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 35x + 2 = 0$,then the value of $(2\alpha - 35)^3 \cdot (2\beta - 35)^3$ is equal to

If $\alpha, \beta$ are the roots of the equation $ax^2 + bx + c = 0$,then the equation whose roots are $\alpha + \frac{1}{\beta}$ and $\beta + \frac{1}{\alpha}$ is