### 5.32.3  Exact values of rational roots of a polynomial : rationalroot

rationalroot takes 1 or 3 arguments : a polynomial and optionally two real numbers α,β.

• If rationalroot has 1 argument, rationalroot returns the list of the value of the rational roots of the polynomial without multiplicity.
• If rationalroot has 3 arguments, rationalroot returns only the rational roots of the polynomial which are in the interval [α,β].

To find the rational roots of 2*x3−3*x2−8*x+12, input:

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

Output :

[2,3/2,-2]

To find the rational roots of 2*x3−3*x2−8*x+12 in [1;2], input:

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

Output :

[2,3/2]

To find the rational roots of 2*x3−3*x2+8*x−12, input:

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

Output :

[3/2]

To find the rational roots of 2*x3−3*x2+8*x−12, input:

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

Output :

[3/2]

To find the rational roots of (3*x−2)2*(2x+1)=18*x3−15*x2−4*x+4, input:

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

Output :

[(-1)/2,2/3]