Roots and poles of a rational function : froot

### 2.30.1 Roots and poles of a rational function : `froot`

`froot` takes a rational function F(x) as argument.
`froot` returns a vector whose components are the roots and the poles of F[x], each one followed by it’s multiplicity.
If `Xcas` can not find the exact values of the roots or poles, it tries to find approximate values if F(x) has numeric coefficients.
Input :

`froot((x```^```5-2*x```^```4+x```^```3)/(x-2))`

Output :

`[1,2,0,3,2,-1]`

Hence, for F(x)=x5−2.x4+x3/x−2 :

- 1 is a root of multiplicity 2,
- 0 is a root of multiplicity 3,
- 2 is a pole of order 1.

Input :

`froot((x```^```3-2*x```^```2+1)/(x-2))`

Output :

`[1,1,(1+sqrt(5))/2,1,(1-sqrt(5))/2,1,2,-1]`

Remark : to have the complex roots and the poles, check `Complex` in the `cas` configuration (red button giving the state line).
Input :

`froot((x```^```2+1)/(x-2))`

Output :

`[-i,1,i,1,2,-1]`