I tried to make a 3D image for $P(x)=x^3+3 x^2-2 x-1$. The set consists of three planes, each tangent to the discriminant surface. But it became too visually complex, partly because [the discriminant](http://mathworld.wolfram.com/PolynomialDiscriminant.html) is complicated. For what it's worth: <hr /> [![enter image description here][1]][1] <br /> <sup> Discriminant surface: blue. </sup> <hr /> Perhaps someone can do better... [1]: https://i.sstatic.net/v4u4i.jpg