Palmer,
I was just reading your Article 593, and working the examples for the 8 cases.
I noticed that case 7 and 8 in this article are the same as the two additional cases in your Article 396, but that the result for R2 in the first additional case in Article 396 doesn't match the result for case 7 in Article 593.
Also, the result for the imaginary part of the roots of the second additional case in Article 396 doesn't match the result for case 8 in Article 593.
The error seems to be in the Article 396 results, and in fact, the R2 result for the first additional case in Article 396 seems to be the square root of the correct result.