Exact roots of a polynomial : roots

### 2.24.19 Exact roots of a polynomial : `roots`

`roots` takes as arguments a symbolic polynomial expression and the name of it’s variable.
`roots` returns a 2 columns matrix : each row is the list of a root of the polynomial and it’s multiplicity.
Examples

- Find the roots of P(x)=x5−2x4+x3.
  Input :
  `roots(x```^```5-2*x```^```4+x```^```3)`
  Output :
  `[[8+3*sqrt(7),1],[8-3*sqrt(7),1],[0,3]]`
- Find the roots of x10−15x8+90x6−270x4+405x2−243=(x2−3)5.
  Input :
  `roots(x```^```10-15*x```^```8+90*x```^```6-270*x```^```4+405*x```^```2-243)`
  Output :
  `[[sqrt(3),5],[-(sqrt(3)),5]]`
- Find the roots of (t3−3).
  Input :
  `roots(t```^```3-1,t)`
  Output :
  `[[(-1+(i)*sqrt(3))/2,1],[(-1-(i)*sqrt(3))/2,1],[1,1]]`