A quick method for intersecting two integer quadratic beziers?

Given two Quadratic Beziers in 2D with integer coordinates, what is the best way to find their intersection point? Early failure is also interesting if they do not overlap. If this simplifies, they can be considered monotonic in both x and y. Only intersections that are represented by the unit as integers of input curves are valid.

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This document explains various methods for finding intersection of curves.

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