If $x^2 - 11x + a$ and $x^2 - 14x + 2a$ have a common factor,then $a = ......$

If the equations $ax^2 + bx + c = 0$ and $cx^2 + bx + a = 0$ $(a \neq c)$ have a common negative root,then the value of $a - b + c$ is:

If the quadratic equations $3x^2 + ax + 1 = 0$ and $2x^2 + bx + 1 = 0$ have a common root,then what is the value of the expression $5ab - 2a^2 - 3b^2$?

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

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:

The value of $a$ for which the equations $x^3+ax+1=0$ and $x^4+ax^2+1=0$ have a common root is