The expressions $x^2 - 11x + a$ and $x^2 - 14x + 2a$ will have a common factor,if $a = $

If $x^2-3ax+14=0$ and $x^2+2ax-16=0$ have a common root,then $a^4+a^2=$

Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $x^2+2px+q=0$ and $\alpha, \frac{1}{\beta}$ are the roots of the equation $ax^2+2bx+c=0$,where $\beta^2 \notin \{-1, 0, 1\}$.
$STATEMENT-1$: $(p^2-q)(b^2-ac) \geq 0$ and
$STATEMENT-2$: $b \neq pa$ or $c \neq qa$.

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

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 $x^2 + bx - 1 = 0$ and $x^2 + x + b = 0$ have a common root different from $-1$,then $|b|$ is equal to