Fundamental Continuity Theorem

Given two univariate polynomials of the same order whose first  coefficients (but not the first ) are 0 where the coefficients of the second approach the corresponding coefficients of the first as limits, the second polynomial will have exactly  roots that increase indefinitely. Furthermore, exactly  roots of the second will approach each root of multiplicity  of the first as a limit.

REFERENCES:

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 4, 1959.