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File:Polynomial roots multiplicity.svg

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English: Graph of the polynomial y = x^3 + 2*x^2 - 7*x + 4 with its roots (zeros) -4 and 1 marked. The root -4 is a 'simple' root (of multiplicity 1), and therefore the graph crosses the x-axis at this root. The root 1 is of even multiplicity and therefore the graph bounces off the x-axis at this root.

The gnuplot 4.4 program which generates this graph:

set terminal svg enhanced size 1000 1000 linewidth 2 fsize 20 set output "polynomial_roots_multiplicity.svg" set xrange [-5:5] set yrange [-10:25] set xzeroaxis linetype -1 set yzeroaxis linetype -1 set key off set label "x = 1" at 2,-2 left set arrow 1 from 1.9,-2 to 1,0 set label "x = -4" at -3,2 left set arrow 2 from -3.1,2 to -4,0

plot x**3 + 2 * x**2 - 7*x + 4 with lines
Date
Source Own work
Author Dov Murik

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9 June 2014

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Date/TimeThumbnailDimensionsUserComment
current03:48, 10 June 2014Thumbnail for version as of 03:48, 10 June 20141,000 × 1,000 (7 KB)דובק1User created page with UploadWizard

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