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 />
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
[![enter image description here][1]][1]
<br />
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
<sup>
Discriminant surface: blue.
</sup>
<hr />
Perhaps someone can do better...

  [1]: https://i.sstatic.net/v4u4i.jpg