Exact values of rational roots of a polynomial :
rationalroot

rationalroot takes 1 or 3 arguments : a polynomial and optionnally two reals numbers $\alpha$,$\beta$.

• 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 [$\alpha$,$\beta$].

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]