If both the roots of $k(6x^2 + 3) + rx + 2x^2 - 1 = 0$ and $6k(2x^2 + 1) + px + 4x^2 - 2 = 0$ are common,then $2r - p$ is equal to

If every pair of the equations $x^2 + px + qr = 0$,$x^2 + qx + rp = 0$,and $x^2 + rx + pq = 0$ have a common root,then the sum of the three common roots 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

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 $\alpha$ is the common root of the quadratic equations $x^2-5x+4a=0$ and $x^2-2ax-8=0$,where $a \in R$,then the value of $\alpha^4-\alpha^3+68$ is

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