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?

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 the equations $ax^2 + bx + c = 0$ $(a, b, c \in R, a \ne 0)$ and $2x^2 + 3x + 4 = 0$ have a common root,then $a : b : c$ equals

If one of the roots of the equations $x^2 + ax + b = 0$ and $x^2 + bx + a = 0$ is common,then the numerical value of $(a + b)$ is

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 $q \neq \beta$)

If $ax^2 + bx + c = 0$ and $bx^2 + cx + a = 0$ have a common root,where $a \neq 0$,then $\frac{a^3 + b^3 + c^3}{abc} = $