The Irminones was an early Germanic proto-tribe, or cultural group. They dwelt in eastern Germany, roughly between the Elbe and Oder Rivers some unknown time in the ancient past (perhaps 500 BC or 1000 BC), until the differentiation of localized Teutonic tribes (Lombards, Marcomanni, Quadi) in that region circa 10 CE.
... case, the parabola does not intersect the x-axis at all.)
Note that when computing roots numerically, the usual form of the quadratic formula is not ideal. See Loss of ...