If the equations $ax^2 + bx + a = 0$ and $x^3 - 2x^2 + 2x - 1 = 0$ have two common roots,then what is the value of $a + b$?

$A$ value of $b$ for which the equations $x^2+bx-1=0$ and $x^2+x+b=0$ have one root in common is

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 $\alpha$ is the common root of the quadratic equations $x^2-5x+4a=0$ and $x^2-2ax-8=0$,where $a \in R$,then the value of $\alpha^4-\alpha^3+68$ is

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:

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?