The roots of the equation $ax^{2} + (4a^{2} - 3b)x - 12ab = 0$ are

Two candidates attempt to solve the equation $x^2 + px + q = 0$. One starts with a wrong value of $p$ and finds the roots to be $2$ and $6$,and the other starts with a wrong value of $q$ and finds the roots to be $2$ and $-9$. The roots of the original equation are

If $\alpha, \beta$ are the roots of ${x^2} + px + q = 0$ and $\alpha + h, \beta + h$ are the roots of ${x^2} + rx + s = 0$,then

If the equations $x^2 + px + 2q = 0$ and $x^2 + qx + 2p = 0$ $(p \ne q)$ have a common root,then the value of $p + q$ is

The equation whose roots are $\frac{1}{3 + \sqrt{2}}$ and $\frac{1}{3 - \sqrt{2}}$ is

The value of $k$ for which one of the roots of $x^2 - x + 3k = 0$ is double of one of the roots of $x^2 - x + k = 0$ is