write a polynomial with the root 3+2i, i-3 ,5

Question

 help asap

Answer 1

First off, note that if a complex number of form a+bi is a root, then so is the

complex conjugate a-bi. 

 

if 3+ 2i is a root, so is 3 - 2i

 

i-3 = -3+i so...

If -3+i is a root, so is -3-i is a root

 

Your roots are:

3+2i, 3-2i, -3+i, -3-i, 5

 

If n is a root of the polynomial p(x) then (x-n) is a factor

 

p(x) = (x-(3+2i))(x-(3-2i))(x-(-3+i))(x-(-3-i))(x-5)

 

p(x) = (x-3-2i)(x-3+2i)(x+3-i)(x+3+i)(x-5)