The least integer $k$ which makes the roots of the equation $x^2 + 5x + k = 0$ imaginary is

If $\alpha$ and $\beta$ are the real roots of the equation $\sqrt{\frac{5x}{x-2}} + \sqrt{\frac{x-2}{5x}} = \frac{29}{10}$ and $\alpha > \beta$,then $\sqrt{\alpha^2 - 11^4 \beta^2} = $

If the set of all $a \in R - \{1\}$,for which the roots of the equation $(1-a)x^2 + 2(a-3)x + 9 = 0$ are positive,is $(-\infty, -\alpha] \cup [\beta, \gamma)$,then $2\alpha + \beta + \gamma$ is equal to . . . . . . .

The number of real roots of the polynomial equation $x^4-x^2+2x-1=0$ is

If $(1 - p)$ is a root of the quadratic equation $x^2 + px + (1 - p) = 0$,then its roots are:

What are the real roots of the equation $x^2 + 5|x| + 4 = 0$?