Question

Is is possible to write a polynomial of degree 4 with zeros at 5, 3 and 8i? Explain your reasoning.

Answer 1

We know that if a polynomial has a complex root then the conjugate is also a root, in this case this means that if the polynomial has a root 8i then the number -8i is also a root. Taking this into account the polynomial that have the roots given would be:

`(x-5)(x-3)(x-8i)(x+8i)`

this is a polynomial of degree 4.