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 the equations $x^2 + ax + 10 = 0$ and $x^2 + bx - 10 = 0$ have a common root,then $a^2 - b^2 = \dots \dots$

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

If the equations $x^2 - 11x + a = 0$ and $x^2 - 14x + 2a = 0$ have a common factor and $a \neq 0$,then what is the common factor?

If the equations $x^2 - cx + d = 0$ and $x^2 - ax + b = 0$ have one common root and the second equation has two equal roots,then $2(b + d) = \dots$

Statement-$I$: If $a, b, c \in R$ and the equations $ax^2 + bx + c = 0$ and $x^2 + 3x + 4 = 0$ have a common root,then $\frac{a+c}{b} = \frac{4}{3}$.
Statement-$II$: If $a_1x^2 + b_1x + c_1 = 0$ and $a_2x^2 + b_2x + c_2 = 0$ have both roots common,then $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$,where $a_1, a_2, b_1, b_2, c_1, c_2 \in R$.