The unique point of intersection is (3, 2), so the repeated root is z = 3 + 2i.
In the case that both of the conics are degenerate, there will be just one point of intersection, corresponding to repeated roots.
Despite
repeated root canal therapy, a diagnosis of chronic apical infection and extensive external inflammatory resorption was reached and both the central permanent incisors were deemed to have a poor prognosis (Figure 1a-b).
However, this is not the case, because in Figure 2b the point of contact corresponds to the once
repeated root of the quadratic equation, e.g.
(6.) Chosack A, Sela J, Cleaton-Jones P: A histological and quantitative histomorphometric study of apexification of non vital permanent incisors of vervet monkeys after
repeated root filling with a calcium hydroxide paste.
Compared with Table 2, the new method shows one integrated SMC value of each pair of
repeated roots. For example, the SMC of the 39/40thmodes is 0.5871.
where R is a rational function of its two arguments, P is a polynomial of degree 3 or 4 with no
repeated roots, and c is a constant.
(The exception involves what mathematicians call "
repeated roots.")
With reference to the complex
repeated roots presented in section Type I(b), the same criterion applies here but with the additional constraint that now n or r = 0 (which implies [b.sub.I][a.sub.R] - [a.sub.I][b.sub.R] = 0 from Equation(7e)) to enforce a solution on the real GA plane.
Modern mathematics defines an "elliptic integral" as any function f which can be expressed in the form f (x) = [[integral].sup.x.sub.c] R,(t, [square root of P(t)]dt, where R is a rational function of its two arguments, P a polynomial of degree 3 or 4 with no
repeated roots, and c is a constant.