Sentence examples for a root of multiplicity from inspiring English sources

If r is a root of multiplicity m, use (c1rn + c2nrn + c3n2rn +... + cmnm-1rn) instead of simply (c1rn).

For an input vector, the algorithm computes a special bivariate polynomial such that each couple is a root of with multiplicity.

(b) If y ¯ 1 is a root of (7) of multiplicity two, then the equilibrium point E 1 is non-hyperbolic and E 3 is a saddle point.

If y ¯ 1 is a root of (7) of multiplicity two, then the equilibrium point E 1 is non-hyperbolic and E 3 is a saddle point.

Furthermore, λ 1 ( 1 ) = 1, λ 2 ( 1 ) > 1 and 0 < λ 1 ( 3 ) < 1, λ 2 ( 3 ) > 1.   (c) If y ¯ 3 is a root of (7) of multiplicity two, then the equilibrium point E 3 is non-hyperbolic and E 1 is a saddle point.

If Δ 3 = 0, Δ 2 = 0 and Δ 1 = 0 then (13) has one real root of multiplicity four.

(e) If Δ 1 = 0 and Δ 2 = 0, then equation (7) has one pair of conjugate imaginary roots and one real root of multiplicity three.  .

If Δ 1 = 0 and Δ 2 = 0, then equation (7) has one pair of conjugate imaginary roots and one real root of multiplicity three.

(h) If Δ 3 = 0, Δ 2 = 0 and Δ 1 = 0 then (13) has one real root of multiplicity four.  .

(d) If Δ 1 = 0 and Δ 2 ≠ 0, then equation (7) has one pair of conjugate imaginary roots and two real roots, one real root of multiplicity one and other one of multiplicity two.

If Δ 1 = 0 and Δ 2 ≠ 0, then equation (7) has one pair of conjugate imaginary roots and two real roots, one real root of multiplicity one and other one of multiplicity two.