Re: Bug in Solve?
- To: mathgroup at smc.vnet.net
- Subject: [mg102966] Re: [mg102921] Bug in Solve?
- From: "David Park" <djmpark at comcast.net>
- Date: Thu, 3 Sep 2009 05:40:27 -0400 (EDT)
- References: <11688861.1251880873838.JavaMail.root@n11>
f[x_] := x^3 - 15 x + 2 Solve[f[x] == 0, x] N[%] // Chop gives the same answers. Solve is returning exact answers but in a form where it is not immediately apparent that they are real. You can obtain approximate values by using N on the result but then you also have to use Chop to get rid of round-off errors in the imaginary values. In some cases, and certainly with higher order polynomials, Solve will give you Root expressions. (Look them up.) These are also exact solutions, which you can convert to approximate solutions with N. Try: f[x_] := x^3 - 15 x + 2 Solve[f[x] == 0, x] FullSimplify[%] N[%] David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: tonysin [mailto:a2mgoog at yahoo.com] I am just trying to learn Mathematica. What am I doing wrong here? I have a very simple equation: x^3 - 15 x + 2 = 0 When I plot it in Mathematica 7, ClearAll[*] f[x_] := x^3 - 15 x + 2 Plot[f[x], {x, -5, 5}] it gives the expected graph of a cubic, with three real roots near -4, 0, and 4. When I NSolve it, NSolve[f[x] == 0, x] it gives {{x -> -3.938}, {x -> 0.133492}, {x -> 3.80451}} which is exactly what you would expect from the graph. But when I Solve it Solve[f[x] == 0, x] it gives this mess {{x -> 5/(-1 + 2 I Sqrt[31])^(1/3) + (-1 + 2 I Sqrt[31])^( 1/3)}, {x -> -((5 (1 + I Sqrt[3]))/( 2 (-1 + 2 I Sqrt[31])^(1/3))) - 1/2 (1 - I Sqrt[3]) (-1 + 2 I Sqrt[31])^(1/3)}, {x -> -(( 5 (1 - I Sqrt[3]))/(2 (-1 + 2 I Sqrt[31])^(1/3))) - 1/2 (1 + I Sqrt[3]) (-1 + 2 I Sqrt[31])^(1/3)}} I don't know how it looks in your font, but that "I" in each solution is the imaginary i. Solve is saying this equation has no real roots, even though the graph clearly shows that all three roots are real. Can someone tell me if I am doing something wrong, or am I expecting something wrong, or if I just can't trust Mathematica? Thanks for any help.