Cubics, hyperbolas and steiner ellipses.

In this article, we will show that for every choice of real numbers a 1 and a 2 , the set (loci) of solutions of all polynomials of the type x 3 + a 2 x 2 + a 1 x + d , where d ∈ R , can be characterized in terms of hyperbolas. Furthermore, relations between such hyperbolas and Steiner ellipses (inellipses and circumellipses) associated with cubics will be pointed out. [ABSTRACT FROM AUTHOR]