what are the complex zeros for the polynomial f(x)=x^3+27

Question

need to find the complex zeros for the following polynomial

f(x)=x^3+27

Answer 1

f(x)=x³+27=(x+3)(x²-3x+9).

x²-3x=-9 satisfies the quadratic,

x²-3x+9/4=-9+9/4=-27/4,

(x-3/2)²=-27/4, x-3/2=±√(-27/4)=±½3i√3.

The real zero is -3, and the complex zeroes are 3/2+½3i√3 and 3/2-½3i√3.

The complex zeroes could be written: (3/2)(1+i√3) and (3/2)(1-i√3).