How do you write a polynomial with zeros 2i, 3i, 1?

1 Answer
Apr 24, 2016

Answer:

#x^5-x^4+13x^3-13x^2+36x-36=0#

Explanation:

Complex roots occur in conjugate pairs. So, the roots are #1, +-2i, +-3i,#. The degree of the polynomial is 5.

Hence, the polynomial equation is

#(x-1)((x-2i)(x+2i))((x-3i)(x+3i))=0#

#(x-1)(x^2+2^2)(x^2+3^2)=0#

Expanding,

#x^5-x^4+13x^3-13x^2+36x-36=0#