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

Let the equations $ax^2-7x+c=0$ and $ax^2+5x-c=0$ have a common root and $ac \neq 0$. If $3$ is a root of $ax^2-7x+c=0$ other than the common root,then the common root of the given equations is

If $ax^2 + bx + c = 0$ and $bx^2 + cx + a = 0$ have a common root and $a, b, c$ are non-zero real numbers,then $\frac{a^3 + b^3 + c^3}{abc} = $

Two distinct polynomials $f(x)$ and $g(x)$ are defined as follows: $f(x)=x^2+ax+2$ and $g(x)=x^2+2x+a$. If the equations $f(x)=0$ and $g(x)=0$ have a common root,then the sum of the roots of the equation $f(x)+g(x)=0$ is:

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

If $p, q, r$ are in $G.P.$ and the equations $p x^{2}+2 q x+r=0$ and $d x^{2}+2 e x+f=0$ have a common root,then show that $\frac{d}{p}, \frac{e}{q}, \frac{f}{r}$ are in $A.P.$