For $a \neq b$,if the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ have a common root,then the value of $a+b=$

If $ax^2 + bx + c = 0$ and $bx^2 + cx + a = 0$ have a common root,where $a \neq 0$,then $\frac{a^3 + b^3 + c^3}{abc} = $

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 $x^2 - 11x + a$ and $x^2 - 14x + 2a$ have a common factor,then $a = ......$

If a root of the equations $x^2 + px + q = 0$ and $x^2 + \alpha x + \beta = 0$ is common,then its value will be (where $p \neq \alpha$ and $q \neq \beta$)

If the equations $x^2 + px + 2q = 0$ and $x^2 + qx + 2p = 0$ $(p \neq q)$ have a common root,then the value of $p + q$ is