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]]