What's the function

Question

the zeros are : 0,6i , -6i 

 

and i think the factors are :

 X(x+6i)(x-6i)

Answer 1

If you have zeros r₁, r₂, and r₃, you construct a function

 

f(x) = A(x - r₁)(x - r₂)(x - r₃)

 

with A ≠ 0.  If you choose A = 1, then

 

f(x) = (x - 0)(x - 6i)([x - (-6i)] = x(x - 6i)(x + 6i)

 

Remember that if you have a complex root, its complex conjugate must also be a root, or you will not end up with real coefficients in the final polynomial. In this problem you have 6i and its complex conjugate -6i, so you have all the roots, and your function is correct.