# Exact values of the complex rational roots of a polynomial: crationalroot

### 5.29.8 Exact values of the complex rational roots of a polynomial: crationalroot

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)=2*x3−3*x2+8*x−12:
Input:

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

Output:

⎡
⎢
⎢
⎣

2 i,

3
2

,−2 i

⎤
⎥
⎥
⎦