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

For what value of $k$ do the equations $2x^2 + kx - 5 = 0$ and $x^2 - 3x - 4 = 0$ have a common root?

If the equations $ax^2 + bx + a = 0$ and $x^3 - 2x^2 + 2x - 1 = 0$ have two common roots,then what is the value of $a + b$?

The quadratic equations $x^2-6x+a=0$ and $x^2-cx+6=0$ have one root in common. If the other roots of the first and second equations are integers and are in the ratio $4:3$,then their common root is

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 $A.P.$

If the equations $2ax^2 - 3bx + 4c = 0$ and $3x^2 - 4x + 5 = 0$ have a common root,then $\left( \frac{a + b}{c} \right)$ is equal to,where $a, b, c \in \mathbb{R}$.