If the equations $2ax^2 - 3bx + 4c = 0$ and $3x^2 - 4x + 5 = 0$ have a common root,then $\frac{a+b}{b+c}$ is equal to $(a, b, c \in R)$.

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 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 quadratic equations $3x^2 - 7x + 2 = 0$ and $kx^2 + 7x - 3 = 0$ have a common root,then the positive value of $k$ is

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

If $x^2+5ax+6=0$ and $x^2+3ax+2=0$ have a common root,then that common root is