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

If the equations $x^2+px+2=0$ and $x^2+x+2p=0$ have a common root,then the sum of the roots of the equation $x^2+2px+8=0$ is

For what value of $a$ do the equations $x^2 - 3x + a = 0$ and $x^2 + ax - 3 = 0$ have a common root?

If the roots of the equations $x^2 + 3x + 2 = 0$ and $x^2 - x + \lambda = 0$ are in the same ratio,then what is the value of $\lambda$?

If the quadratic equations $x^2 - 7x + 3c = 0$ and $x^2 + x - 5c = 0$ have a common root,then for a non-zero real value of $c$,the sign of the expression $x^2 - 3x + c$ is:

If $\alpha$ is a common root of $x^2-5x+\lambda=0$ and $x^2-8x-2\lambda=0$ $(\lambda \neq 0)$ and $\beta, \gamma$ are the other roots of them respectively,then $\alpha+\beta+\gamma+\lambda=$