### 23.3.4 Numeric roots of a polynomial

The proot command numerically finds the roots of a squarefree polynomial.

- proot takes P, a squarefree polynomial, either in symbolic form or as a list of polynomial coefficients (written by decreasing order).
- proot(P) returns a list of the numeric roots of P.

#### Examples

Find the numeric roots of P(x)=x3+1.

proot([1,0,0,1])

or:

proot(x^3+1)

| ⎡ ⎣ | −1.0,0.5−0.866025403784 i,0.5+0.866025403784 i | ⎤ ⎦

Find the numeric roots of x2−3.

proot([1,0,-3])

or:

proot(x^2-3)

| ⎡ ⎣ | −1.73205080757,1.73205080757 | ⎤ ⎦