### 11.3.5 Exact values of rational roots of a polynomial

The rationalroot command finds rational roots of polynomials.

- rationalroot takes one mandatory and two optional arguments:
  - P, a polynomial.
  - Optionally, α and β, two real numbers.
- rationalroot(P) returns the list of the value of the rational roots of P without multiplicity.
- rationalroot(P,α,β) returns the list of the rational roots of P which are in the interval [α,β].

#### Examples

Find the rational roots of 2x3−3x2−8x+12:

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

| ⎡ ⎢ ⎢ ⎣ | 2,−2, |
3
2
| ⎤ ⎥ ⎥ ⎦

Find the rational roots of 2x3−3x2−8x+12 in [1,2]:

rationalroot(2*x^3-3*x^2-8*x+12,1,2)

| ⎡ ⎢ ⎢ ⎣ | 2, |
3
2
| ⎤ ⎥ ⎥ ⎦

Find the rational roots of 2x3−3x2+8x−12:

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

| ⎡ ⎢ ⎢ ⎣ |
3
2
| ⎤ ⎥ ⎥ ⎦

Find the rational roots of 2x3−3x2+8x−12:

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

| ⎡ ⎢ ⎢ ⎣ |
3
2
| ⎤ ⎥ ⎥ ⎦

Find the rational roots of (3x−2)2(2x+1)=18x3−15x2−4x+4:

rationalroot(18*x^3-15*x^2-4*x+4)

| ⎡ ⎢ ⎢ ⎣ | − |
1
2
| , |
2
3
| ⎤ ⎥ ⎥ ⎦