# Coefficients of a polynomial defined by its roots: pcoeff pcoef

### 5.27.23 Coefficients of a polynomial defined by its roots: pcoeff pcoef

The pcoeff command reconstructs a polynomial from its roots.
pcoef is a synonym for pcoeff.

- pcoeff takes one argument:
  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.

Input:

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

Output:

[1,-6,11,-6,0,0]

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