Consider the set of cubic polynomials, x³ + (1-p)x² + px + 1, p ∈ Z. Then consider the set of triangles formed by the roots of these polynomials in the complex plane. Find the value of p which maximizes the area of such triangles.

The required maximum value of p is approximately equal to 4.542 and, the corresponding maximum area is approximately equal to 2.736.

Posted by K Sengupta on 2022-06-19 00:35:15