Using Mathematica to solve for the roots of a characteristic equation .

Example 1 :

f[r_] = 9r^3 - 30r^2 + 19r + 10

10 + 19 r - 30 r^2 + 9 r^3

Note :   Remember to press Shift + Enter at the end of each line of mathematics in Mathematica, plain Enter won ' t do .

One method is to use Solve to look for exact solutions :

Solve[f[r] 0, r]

{{r -1/3}, {r5/3}, {r2}}

Another method is to use NSolve to look for numerical (approximate) solutions :

NSolve[f[r] 0, r]

RowBox[{{, RowBox[{RowBox[{{, RowBox[{r, , RowBox[{-, 0.333333}]}], }}], ,, RowBox[{{, RowBox[{r, , 1.66667}], }}], ,, RowBox[{{, RowBox[{r, , 2.}], }}]}], }}]

Example 2 :

g[r_] = r^4 + 4r^3 - 16r - 16

-16 - 16 r + 4 r^3 + r^4

Solve[g[r] 0, r]

{{r -2}, {r -2}, {r -2}, {r2}}


Created by Mathematica  (January 30, 2004)