The value of $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$ is

If $\alpha, \beta$ are the roots of $ax^{2}+bx+c=0$ $(a \neq 0)$ and $\alpha+h, \beta+h$ are the roots of $px^{2}+qx+r=0$ $(p \neq 0),$ then the ratio of the squares of their discriminants is

$A$ number is the reciprocal of the other. If the arithmetic mean of the two numbers is $\frac{13}{12}$,then the numbers are:

If the sum of two particular roots of the equation $x^4-4x^3-7x^2+22x+24=0$ is equal to the sum of the remaining two roots,then the sum of the cubes of all the roots of this equation is

If $|{x^2} - x - 6| = x + 2$,then the values of $x$ are

$\alpha$ is a root of the equation $\frac{x-1}{\sqrt{2x^2-5x+2}} = \frac{41}{60}$. If $-\frac{1}{2} < \alpha < 0$,then $\alpha = $