If the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ $(a \neq b)$ have a common root,then $a+b$ is equal to

If every pair of the equations $x^2 + px + qr = 0$,$x^2 + qx + rp = 0$,and $x^2 + rx + pq = 0$ have a common root,then the sum of the three common roots is:

If the equations $k(6x^2 + 3) + rx + 2x^2 - 1 = 0$ and $6k(2x^2 + 1) + px + 4x^2 - 2 = 0$ have common roots,then $2r - p = \dots$

The equations $2x^2+ax-2=0$ and $x^2+x+2a=0$ have exactly one common root. If $a \neq 0$,then one of the roots of the equation $ax^2-4x-2a=0$ is

Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $x^2+2px+q=0$ and $\alpha, \frac{1}{\beta}$ are the roots of the equation $ax^2+2bx+c=0$,where $\beta^2 \notin \{-1, 0, 1\}$.
$STATEMENT-1$: $(p^2-q)(b^2-ac) \geq 0$ and
$STATEMENT-2$: $b \neq pa$ or $c \neq qa$.

If a root of the equations $x^2 + px + q = 0$ and $x^2 + \alpha x + \beta = 0$ is common,then its value will be (where $p \neq \alpha$ and $q \neq \beta$)