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.
Fundamental Continuity Theorem
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 4, 1959.Referenced on Wolfram|Alpha
Fundamental Continuity TheoremCite this as:
Weisstein, Eric W. "Fundamental Continuity Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FundamentalContinuityTheorem.html