Lill method folding example (original) (raw)

Lill method folding example Using Lill's method with paper folding to find the real roots of 3x³+2x²−7x+2 by CMG Lee. For each root, the start point (black circle) and end point (black square) are reflected onto lines passing through reflections of the start and end points in the second and third segments (faint circle and square) and parallel to the them (grey lines). The axis of reflection (dash-dot line) defines the path corresponding to the root, given by the negative of the gradient or slope of the first segment, m. 3 2 3 2 7 2 m=−1∴x=1 m=2∴x=−2 m=−1/3∴x=1/3 3x³+2x²−7x+2 = 0