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
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