The expressions $x^2 - 11x + a$ and $x^2 - 14x + 2a$ will have a common factor,if $a = $

If both the roots of $k(6x^2 + 3) + rx + 2x^2 - 1 = 0$ and $6k(2x^2 + 1) + px + 4x^2 - 2 = 0$ are common,then $2r - p$ is equal to

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 $(a, b, c \in R)$.

The equations $x^2-ax+b=0$ and $x^2+bx-a=0$ have a common root. Then:

Let $a \ne b, c \ne 0$. If the equations $x^2 + ax + bc = 0$ and $x^2 + bx + ac = 0$ have a common root,then:
Statement-$1$: The equation of the other roots is $x^2 + cx + ab = 0$.
Statement-$2$: $a + b + c = 0$.

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?