Question

Write the equation of a polynomial function of degree 5 with roots 1, 2i, and 3i.

Answer 1

Step-by-step explanation:

given 2i and 3i are the roots of equation then thier conjugates are also roots of the equation

so 1,2i,-2i,3i,-3i

are the roots then equation is

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

(x-1)(x^2+4)(x^2+9)=0

(x-1)(x^4+13x^2+36)=0

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

this is the required polynomial equation