If the equations $x^2 + bx + c = 0$ and $x^2 + cx + b = 0$ $(b \neq c)$ have a common root,then:

If the equations $x^2+px+2=0$ and $x^2+x+2p=0$ have a common root,then the sum of the roots of the equation $x^2+2px+8=0$ is

If the two equations $x^2 - cx + d = 0$ and $x^2 - ax + b = 0$ have one common root and the second equation has equal roots,then $2(b + d) = $

If the quadratic equations $x^2 - 7x + 3c = 0$ and $x^2 + x - 5c = 0$ have a common root,then for a non-zero real value of $c$,the sign of the expression $x^2 - 3x + c$ is:

If the equations $x^2 + px + q = 0$ and $x^2 + qx + p = 0$ have a common root,then $p + q + 1 = $

If $a, b, c$ are in $G.P.$,then the equations $ax^2 + 2bx + c = 0$ and $dx^2 + 2ex + f = 0$ have a common root if $\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in