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?

Let $\lambda \neq 0$ be in $\mathbb{R}$. If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+2\lambda=0$,and $\alpha$ and $\gamma$ are the roots of the equation $3x^{2}-10x+27\lambda=0$,then $\frac{\beta\gamma}{\lambda}$ is equal to:

Let $a, b, c, d \in \mathbb{R}$. If the equations $2bx^2 + 3cx - d = 0$ and $2ax^2 + 3bx + 4c = 0$ have a common root and $\frac{4bc + ad}{k(b^2 - ac)} = \frac{bd + 4c^2}{4bc + ad}$,then $k =$

If every pair of the equations $x^2 + px + qr = 0$,$x^2 + qx + rp = 0$,and $x^2 + rx + pq = 0$ have a common root,then the sum of the three common roots is:

If $2x^2+3x-2=0$ and $3x^2+ax-2=0$ have one common root,then the sum of all possible values of $a$ is (in $.5$)

If $3x^2 - 7x + 2 = 0$ and $15x^2 - 11x + a = 0$ have a common root and $a$ is a positive real number,then the sum of the roots of the equation $15x^2 - ax + 7 = 0$ is: