# What does the notation $Dx(a-bi-x)$ mean?

Sorry for completely newbie question, but could not the answer anywhere else. On the Wikipedia page about "Steiner inellipse" there is the following notation equating roots of cubic polynomial and roots of its derivative:

$Dx(1 + 7i − x)(7 + 5i − x)(3 + i − x) = (13/3 + 11/3i − x)(3 + 5i − x).$

What does the 'Dx' symbol mean here?

• The leading order term of the derivative should be $-3x^2$ though, so something does not quite fit; probably a factor of $(-3)$ is missing. – fuglede Jan 13 '14 at 14:04
• Probably should be $D_x$, but the caption of a figure does not admit Latex. – GEdgar Jan 13 '14 at 14:10
• For those confused by the wording of the question: I've edited the Wikipedia article to have the $x$ as a subscript, as well as added the missing $-3$. – fuglede Jan 13 '14 at 14:12
• @ChristopherErnst, Thanks for the answer. I thought that roots of derivative somehow can be obtained directly from the cubic roots. But one need to do a usual differentiantion. – Albert Jan 13 '14 at 14:23
• @rschwieb, i deleted the comment and reposted as the answer. Thank you. – Eleven-Eleven Jan 13 '14 at 16:58

The Dx symbol means that the derivative of the cubic polynomial $$((1+7i)−x)((7+5i)−x)((3+i)−x)$$ is $$-3((13/3+11/3i)−x)((3+5i)−x)$$