If a root of the equation $ax^2 + bx + c = 0$ is the reciprocal of a root of the equation $a'x^2 + b'x + c' = 0$,then:

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 $x^2+3x-2k=0$ and $x^2-2x-7k=0$ have a non-zero common root,then the positive root of the equation $kx^2+(k+2)x-(k+1)=0$ is

Let $E_1 \equiv ax^2+bx+c$,$E_2 \equiv bx^2+cx+a$,$E_3 \equiv cx^2+bx+a$ and $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}=3$. If these quadratic expressions have a common zero,then the quadratic expression having zeroes that are common to $E_2$ and $E_3$ and different from the zeroes of $E_1$ is

If the equations $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0$,where $a, b, c \in R$,have the same roots,then what is the ratio $a : b : c$?

If the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ $(a \neq b)$ have a common root,then $a+b$ is equal to