### 11.1.23 Coefficients of a polynomial defined by its roots

The pcoeff or pcoef command reconstructs a polynomial from its roots.

- pcoeff takes roots, a list of the roots of a polynomial P.
- pcoeff(roots) returns the monic polynomial having these roots, represented as the list of its coefficients in decreasing order.

#### Example

pcoef([1,2,0,0,3])

[1,−6,11,−6,0,0] |  |  |  |  |  |  |  |  |  |

i.e. (x−1)(x−2)(x2)(x−3)=x5−6x4+11x3−6x2.