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===Upper bound on the magnitude of the roots===
The [[absolute value|modulus]] of the roots of a quadratic <math>ax^2+bx+c</math> can be no greater than <math>\frac{\max(|a|, |b|, |c|)}{|a|}\times \phi, </math> where <math>\phi</math> is the [[golden ratio]] <math>\frac{1+\sqrt{5}}{2}.</math><ref>{{Cite journal |last=Lord |first=Nick |date=2007-11-01 |title=Golden Bounds for the Roots of Quadratic Equations |url=https://doi.org/10.2307/40378441 |journal=[[The Mathematical Gazette]] |volume=91 |issue=522 |pages=549 |doi=10.1017/S0025557200182324 |jstor=40378441 |url-access=subscription }}</ref>
==The square root of a univariate quadratic function==
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