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 $(a, b, c \in R)$.

If $\alpha, \beta$ and $\gamma$ are three consecutive terms of a non-constant $G.P.$ such that the equations $\alpha x^2 + 2\beta x + \gamma = 0$ and $x^2 + x - 1 = 0$ have a common root,then $\alpha(\beta + \gamma)$ is equal to

If every pair of the equations $x^2 + px + qr = 0$,$x^2 + qx + rp = 0$,and $x^2 + rx + pq = 0$ have a common root,then the sum of the three common roots is:

If the equations $ax^2 + bx + c = 0$ and $cx^2 + bx + a = 0$ $(a \neq c)$ have a common negative root,then the value of $a - b + c$ is:

If $ax^2 + bx + c = 0$ and $bx^2 + cx + a = 0$ have a common root and $a, b, c$ are non-zero real numbers,then $\frac{a^3 + b^3 + c^3}{abc} = $

If $\alpha$ is the common root of the quadratic equations $x^2-5x+4a=0$ and $x^2-2ax-8=0$,where $a \in R$,then the value of $\alpha^4-\alpha^3+68$ is