Question

Find the rational zeros and then the other zeros f(x)=x^3+27

Answer 1

The sum of cubes is a special form that has the factorization

... x³ + a³ = (x +a)(x² -ax +a²)

For a=3, the factorization is

... x³ + 3³ = (x +3)(x² -3x +9)

The first of these factors is zero for x=-3. The second of these factors is zero for

... x = (3±√-27)/2 = (3/2)(1±i√3) . . . . . from the quadratic formula

The zeros are {-3, (3/2)(1-i√3), (3/2)(1+i√3)}.