repeated root

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Multiple Root

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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.

Graphical solution of the monic quadratic equation with complex coefficients

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).

Indications for the use of auto-transplantation of teeth in the child and adolescent

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.

Transitional processes as a tool for revealing universe's hidden dimensions

(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.

Single visit apexification with mineral trioxide aggregate

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.

Study on repeated-root modes in substructure modal composition analysis

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.

Certain integral involving inverse hyperbolic function

(The exception involves what mathematicians call "repeated roots.")

Solving the dual IRR puzzle

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.

Visualising the roots of quadratic equations with complex coefficients

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.

Certain indefinite integral associate to elliptic integral and complex argument

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