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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT 
-1 7 "Example" }}{PARA 0 "" 0 "" {TEXT -1 36 "Show graphically that th
e zeros of  " }{XPPEDIT 18 0 "z^9+2*z^5+4*z^3+9;" "6#,**$)%\"zG\"\"*\"
\"\"F(*&\"\"#F(*$)F&\"\"&F(F(F(*&\"\"%F(*$)F&\"\"$F(F(F(F'F(" }{TEXT 
-1 43 "  lie between the circles of radii 1 and 2." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 8 "Solution" 
}}{PARA 0 "" 0 "" {TEXT -1 38 "First solve for the zeros numerically:
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "s:= [evalf(solve(z^9+2*z
^5+4*z^3+9=0,z))];" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 82 "Cov
ert into rectangular coordinates; plot the points and circles of radii
 1 and 2:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "l:=map(z->[Re(z
),Im(z)],s):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "p:=plot(l,style=poi
nt,symbol=circle):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "c:=plot([[cos
(t),sin(t),t=0..2*Pi],[2*cos(t),2*sin(t),t=0..2*Pi]]):" }}}{PARA 0 "" 
0 "" {TEXT -1 26 "Display them all together:" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 
"display([p,c]);" }}}{EXCHG }}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }
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