Question

Write the polynomial equations with zero at -5,0 and 3i

Answer 1

We are given that the zeroes are at
{-5, 0 , 3i}.
By the conjugate pair theorem, -3i, the conjugate of 3i, is automatically a zero for polynomials with real coefficients.

The factors of the polynomial are:
(x+5), x, (x+3i) and (x-3i)
The last two factors multiply to give a real quadratic factor of x^2+9.

Therefore the polynomial is of the form 
f(x)=ax(x+5)(x^2+9)
where a is any non-zero real constant.