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

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 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 $x^2 + ax + 10 = 0$ and $x^2 + bx - 10 = 0$ have a common root,then $a^2 - b^2 = \dots \dots$

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