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

Find the coordinates of the point on the curve $$y = {x \over {1 + {x^2}}}$$
where the tangent to the curve has the greatest slope.

The points z₁, z₂, z₃, z₄ in the complex plane are the vertices of a parallelogram taken in order if and only if