If both the roots of $k(6x^2 + 3) + rx + 2x^2 - 1 = 0$ and $6k(2x^2 + 1) + px + 4x^2 - 2 = 0$ are common,then $2r - p$ is equal to

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

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

Let $a, b, c, d \in \mathbb{R}$. If the equations $2bx^2 + 3cx - d = 0$ and $2ax^2 + 3bx + 4c = 0$ have a common root and $\frac{4bc + ad}{k(b^2 - ac)} = \frac{bd + 4c^2}{4bc + ad}$,then $k =$

For what value of $k$ do the equations $2x^2 + kx - 5 = 0$ and $x^2 - 3x - 4 = 0$ have a common root?