Question

9. Write a function with the given characteristics.
A polynomial with rational coefficients having roots 3, 3, and 3 − i
Help Please

Answer 1

If it has 3-i as a root, then it will have 3+i as a root

Answer 2

Just expand
\[
(x-3)^2 (x-(3+i)) (x-(3-i))
\]

Answer 3

Are you here

Answer 4

For example
\[
(x-3)^2=x^2-6 x+9
\]
That should be easy

Answer 5

Also notice that
\[
(x-(a-i b)) (x-(a+i b))=((x-a)-i b) ((x-a)+i b)=\\(x-a)^2-(i b)^2=a^2-2 a x+b^2+x^2
\]

Answer 6

Use the above to expand
\[
(x-(3+i)) (x-(3-i)
\]

Answer 7

Then multiply the two expansions above and you will get your polynomial

Answer 8

sorry and im confused