Question

Find the polynomial from zeros
Zeros are 3i and 2-i

Answer 1

Explanation:

complex numbers always come in pairs. So you have 4 roots to this polynomial

y = (x - 3i)(x + 3i)(x - 2 + i)(x - 2 - i)

y = (x^2 - 9i^2)( (x - 2)^2 + i)( (x - 2)^2 - i)

y = (x^2 + 9) [( x - 2)^2 - i^2]

y = (x^2 + 9) [x^2 - 4x + 4 + 1]

y = (x^2 + 9) (x^2 - 4x + 5)

y = (x^4 - 4x^3 + 14x^2 - 36x + 45)

The graph is below. Notice it never crosses the x axis which you could have predicted from all the complex roots.