Question

How do you write a polynomial function of least degree with integral coefficients that has the given zeroes 4, -1, -3i?

Answer 1

`p(z) = z^4 - 3z^3 + 5z^2 - 27z -36`

Explanation:

`p(z) = (z - 4)(z + 1)(z - 3i)(z + 3i)`

`= (z^2 -3z - 4)(z^2 + 9)`

`= z^4 - 3z^3 -4z^2 + 9z^2 - 27z -36`