Exact values of the complex rational roots of a polynomial

### 11.4.7 Exact values of the complex rational roots of a polynomial

The crationalroot command finds complex rational roots of polynomials.

- crationalroot takes one mandatory and two optional arguments:
  - P, a polynomial.
  - Optionally, α and β, two complex numbers.
- crationalroot(P) returns the list of the value of the rational roots of P without multiplicity.
- crationalroot(P,α,β) returns the list of the rational roots of P which are in the rectangle with sides parallel to the axis having [α,β] as opposite vertices.

#### Example

Find the rational complex roots of (x2+4)(2x−3)=2x3−3x2+8x−12:

crationalroot(2*x^3-3*x^2+8*x-12)

| ⎡ ⎢ ⎢ ⎣ | 2 i, |
3
2
| ,−2 i | ⎤ ⎥ ⎥ ⎦