If $p$ and $q$ are the roots of the equation $x^2 + pq = (p + 1)x$,then $q=$

Let $\alpha$ and $\beta$ be the roots of the equation $p x^2 + q x + r = 0$,where $p \neq 0$. If $p, q, r$ are in $AP$ and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$,then the value of $|\alpha - \beta|$ is

If $p$ and $q$ are the roots of $x^2 + px + q = 0$,then

Suppose the quadratic polynomial $p(x)=ax^2+bx+c$ has positive coefficients $a, b, c$ such that $b-a=c-b$. If $p(x)=0$ has integer roots $\alpha$ and $\beta$,then what could be the possible value of $\alpha+\beta+\alpha\beta$ if $0 \leq \alpha+\beta+\alpha\beta \leq 8$?

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is $2$. Then the roots of the equation are:

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is