If $$x-r$$ is a factor of the polynomial $$f\left( x \right) = {a_n}{x^4} + ..... + {a_0},$$ repeated $$m$$ times $$\left( {1 < m \le n} \right)$$, then $$r$$ is a root of $$\left( x \right) = 0$$ repeated $$m$$ times.

If $$a+b+c=0$$, then the quadratic equation $$3a{x^2} + 2bx + c = 0$$ has

The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing for values of $$x\left( {x \ne 0} \right)$$ satisfying the inequalities ......... and monotonically decreasing for values of $$x$$ satisfying the inequalities ............

The larger of $$\cos \left( {In\,\,\theta } \right)$$ and $$In $$ $$\left( {\cos \,\,\theta } \right)$$ If $${e^{ - \pi /2}} < \theta < {\pi \over 2}$$ is ..................