If one root is square of the other root of the equation $${x^2} + px + q = 0$$, then the realation between $$p$$ and $$q$$ is

If $$\,\alpha \in \left( {0,{\pi \over 2}} \right)\,\,then\,\,\sqrt {{x^2} + x} + {{{{\tan }^2}\alpha } \over {\sqrt {{x^2} + x} }}$$ is always greater than or equal to

The set of all real numbers x for which $${x^2} - \left| {x + 2} \right| + x > 0$$, is

If $${a_1},{a_2}.......,{a_n}$$ are positive real numbers whose product is a fixed number c, then the minimum value of $${a_1} + {a_2} + ..... + {a_{n - 1}} + 2{a_n}$$ is