Exact roots of a polynomial : roots

### 5.25.19 Exact roots of a polynomial : roots

roots takes as arguments a symbolic polynomial expression and the name of its variable.
roots returns a 2 columns matrix : each row is the list of a root of the polynomial and its 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 t3−1.
  Input :
  roots(t`^`3-1,t)
  Output :
  [[(-1+(i)*sqrt(3))/2,1],[(-1-(i)*sqrt(3))/2,1],[1,1]]