The equations $x^2-ax+b=0$ and $x^2+bx-a=0$ have a common root. Then:

If $\alpha, \beta$ and $\gamma$ are three consecutive terms of a non-constant $G.P.$ such that the equations $\alpha x^2 + 2\beta x + \gamma = 0$ and $x^2 + x - 1 = 0$ have a common root,then $\alpha(\beta + \gamma)$ is equal to

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 ${x^2} + ax + 10 = 0$ and ${x^2} + bx - 10 = 0$ have a common root,then ${a^2} - {b^2}$ is equal to

If $x^2+5ax+6=0$ and $x^2+3ax+2=0$ have a common root,then that common root is