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

If $f(x)=x^2+ax+2=0$ and $g(x)=x^2+2x+a=0$ have only one real common root,then the sum of the roots of $f(x)+g(x)=0$ is

Number of roots common to the equations $x^3+x^2-2x-2=0$ and $x^3-x^2-2x+2=0$ is

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

The quadratic equations $x^2 - 6x + a = 0$ and $x^2 - cx + 6 = 0$ have a common root. The other roots of the first and second equations are integers in the ratio $4:3$. Find the common root.

If $a, b, c$ are in $A$.$P$. and if the equations $(b-c) x^2+(c-a) x+(a-b)=0$ and $2(c+a) x^2+(b+c) x=0$ have a common root, then