~v200 200 ~w67 4 476 752 0 319 0 0 ~f? 14 12 10
? 2 0 1 0 ? ? ? "Arial" ? ? ? 0 ? 0 0
"Times" 12 ? ? 6 0 c n 102 0 0 0 k 288
i"NEWTONS  METHOD"
-2 1 26177 26178 26115 26178 1 1 1 1 0 0
0 0 -1 0 0 -1 -1 -1 -1 -1 0 1 ? ? 
~Q
]|Expr|[#b @`bb#_b#_b#_})6# b'3" *|: ;bP8&c0!*This notebook uses|
  | numerical factorization to find roots of a cubic,N|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?v0 (a)~p0
1 ~V?c4 (i)~p0
1 ~V?v0 (y)~p0
1 ~V?v0 (x)~p0
1 ~V?c1 ('p)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$@["! ) # b$@|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})## b$@" *|: ;bP8&c0!*Input coefficients|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~A(a_3=0.5)~p0
0 ~d~A(a_2=-3)~p0
255 ~d~A(a_1=-2)~p0
255 ~d~A(a_0=6)~p0
255 ~d~A(y=a_3*x^3+a_2*x^2+a_1*x+a_0)~p1
0 ~d~A(y=0.5*x^3-3*x^2-2*x+6)~p0
1 ~sb/_!!   }
$&!  c#T"!c"L$_c/__c/__}
^ _~A(0=0.5*x^3-3*x^2-2*~
 x+6)~p0
2 ~sb/_!!   }
b00(!  c#T" c'8 _c/__c/__!"}
^ _~A(y=0)~p0
255 ~A(0=1/2*(x-1.2203843196683595)*(x+1.5527991074306282)*(x-6.3324147877622687))~p0
3 ~sb/_!!   }
'&! "c#T"!c"L$_c/__c/__}
^ _~A(x=1.2203843196683595)~p0
4 ~sb/_!!   }
)-!  c#T"!c"H$!c"L" c'8 _c/__c/__! !}
^ _~A(x_1=x)~p0
5 ~A(x=-1.5527991074306282)~p0
4 ~sb/_!!   }
)-!  c#T"!c"H$"c"L" c'8 _c/__c/__! !}
^ _~A(x_2=x)~p0
5 ~A(x=6.3324147877622687)~p0
4 ~sb/_!!   }
)-!  c#T"!c"H$#c"L" c'8 _c/__c/__! !}
^ _~A(x_3=x)~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$@["! ) # b$@|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})## b$@" *|: ;bP8&c0!*Output roots|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~A(x_1=1.2203843196683595)~p0
0 ~d~sb/_!!   }
b00(!  c#T"!c'8 _c/__c/__!"}
^ _~A(x_2=-1.5527991074306282)~p0
0 ~d~sb/_!!   }
b00(!  c#T"!c'8 _c/__c/__!"}
^ _~A(x_3=6.3324147877622687)~p0
0 ~d~sb/_!!   }
b00(!  c#T"!c'8 _c/__c/__!"}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_})!# b"T["! ) # b"T|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})b I# b"T" *|: ;bP8&c0!*Illustration|
  |                                        |
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~G1 1 230 362
1 1 4 2 10
(-3...8):(-21...11):(?=0...2*'p):('p/~
 5):(10)~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})## b"0" *|: ;bP8&c0!*given function|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~L1 255 ? (x,y):(x=left...right)~p0
1 ~gc0 75 ? 0 -4096 -6016 0
2080 -3836 -3608 0
3120 -3706 -2569 0
5201 -3446 -801 0
6241 -3316 -65 0
7411 -3170 654 0
8321 -3056 1135 0
9362 -2926 1607 0
10272 -2812 1953 0
11442 -2666 2313 0
12482 -2536 2556 0
13213 -2444 2685 0
13653 -2389 2748 0
13994 -2347 2788 0
14563 -2276 2841 0
15213 -2194 2880 0
15603 -2146 2893 0
16513 -2032 2891 0
16952 -1977 2876 0
17409 -1920 2851 0
17684 -1885 2831 0
17927 -1855 2811 0
18074 -1837 2798 0
18317 -1806 2774 0
18724 -1755 2728 0
19894 -1609 2559 0
20804 -1495 2394 0
22755 -1252 1951 0
24965 -975 1334 0
27046 -715 674 0
28086 -585 326 0
30166 -325 -386 0
31207 -195 -742 0
32377 -49 -1135 0
33287 65 -1433 0
34327 195 -1760 0
35238 309 -2031 0
36408 455 -2356 0
37448 585 -2617 0
38618 731 -2875 0
39529 845 -3045 0
40179 926 -3149 0
40569 975 -3203 0
40910 1018 -3246 0
41479 1089 -3308 0
42649 1235 -3389 0
43299 1316 -3408 0
43690 1365 -3409 0
44128 1420 -3401 0
44402 1454 -3390 0
44860 1512 -3365 0
45770 1625 -3279 0
46420 1707 -3189 0
46810 1755 -3122 0
47151 1798 -3056 0
47720 1869 -2930 0
48891 2015 -2603 0
49931 2145 -2234 0
52011 2405 -1252 0
53052 2536 -632 0
53962 2649 -15 0
55132 2796 885 0
57343 3072 2935 0
60203 3429 6318 0
63584 3852 11490 0
63974 3901 12174 0
63998 3904 12217 0
64022 3907 12260 0
64034 3908 12281 0
64037 3909 12287 0
64040 -32768 -32768 0
64046 -32768 -32768 0
64071 -32768 -32768 0
64169 -32768 -32768 0
65535 -32768 -32768 0
~
 ~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})!# b"0" *|: ;bP8&c0!*roots|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~S17 ? 16711680 ? ? (x_1,0):(?):(8)~p0
1 ~gc-1 1 ? 0 -953 1280 0
~S17 ? 16711680 ? ? (x_2,0):(?):(8)~p0
1 ~gc-1 1 ? 0 -3018 1280 0
~S17 ? 16711680 ? ? (x_3,0):(?):(8)~p0
1 ~gc-1 1 ? 0 2854 1280 0
~Q
]|Expr|[#b @`bb#_b#_b#_})!# b"0" *|: ;bP8&c0!*declarations|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?c64 (left)~p0
1 ~V?c65 (right)~p0
1 ~V?c66 (bottom)~p0
1 ~V?c67 (top)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b"0" *|: ;bP8&c0!*axes and grids|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~X1 0 (x,0):(x=left...right):(x)~p0
1 ~gc1 2 ? 0 -4096 1280 0
65535 4096 1280 0
~X2 0 (0,y):(y=bottom...~
 top):(y)~p0
1 ~gc1 2 ? 0 -1862 -4096 0
65535 -1862 4096 0
~R11184810 ? (x,y):(~
 y=bottom...top):(x=left...right):(0)~p0
1 ~gc1 2 ? 0 -3351 -4096 0
65535 -3351 4096 0
~gc1 2 ? 0 -1862 -4096 0
65535 -1862 4096 0
~gc1 2 ? 0 -372 -4096 0
65535 -372 4096 0
~gc1 2 ? 0 1117 -4096 0
65535 1117 4096 0
~gc1 2 ? 0 2607 -4096 0
65535 2607 4096 0
~
 ~R11184810 ? (x,y):(x=left...right):(y=bottom...top):(0)~p0
1 ~gc1 2 ? 0 -4096 -3840 0
65535 4096 -3840 0
~gc1 2 ? 0 -4096 -1280 0
65535 4096 -1280 0
~gc1 2 ? 0 -4096 1280 0
65535 4096 1280 0
~gc1 2 ? 0 -4096 3840 0
65535 4096 3840 0
~t~p0
1 ~c6
12 -1 11 -1 7 -1 1 -1 8 -1 9 -1 10 -1 ~c2
13 -1 12 -1 14 -1 ~c1
15 -1 13 -1 ~c1
16 -1 15 -1 ~c1
18 -1 15 -1 ~c1
20 -1 15 -1 ~c2
23 -1 17 -1 16 -1 ~c2
24 -1 19 -1 18 -1 ~c2
25 -1 21 -1 20 -1 ~e