For how many values $a \in \mathbb{C}$,do the equations $x^2-8x+7=0$ and $x^2-2ax+49=0$ have a common root?

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}=$

If $p, q, r$ are in $G.P.$ and the equations $p x^{2}+2 q x+r=0$ and $d x^{2}+2 e x+f=0$ have a common root,then show that $\frac{d}{p}, \frac{e}{q}, \frac{f}{r}$ are in $A.P.$

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

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 $2r - p = \dots$

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