Rational Roots (C)

Suppose that all the coefficients of a polynomial p(z) are integers. If m and n are integers with no common factors and p(m/n) = 0 then m divides the constant term in p and n divides the leading coeficient.

Observe that every polynomial with rational coeffients is a polynomial with integer coefficients divided by a fixed integer, namely the least common multiple of its coefficients.

Exercises List all the possible rational roots of

1.

z⁹ + 6z + 6;

2.

z¹2 -44z³ - 12;

3.

4z⁴ + 9z - 2;

4.

(4/3)z⁹ + 6z² + 11;