Did I do this right?

Question

I have to make a polynomial funtion out of 2, 4+i, 4-i

i got

(x-2)(x^2-16i)

=x^3-32ix-2x^2+32i

Answer 1

I get (x-2)(x² - 8x + 17)

If 4+i and 4-i are two roots, then multiply (x - (4+i)) (x - (4-i)) =

x² - 4x - ix - 4x + ix + 16 - i² =

x² - 8x + 16 - (-1) =

x² - 8x + 17

I'll leave multiplying this by (x-2) to you!

Hope that helped!

~ ♥ ~

Answer 2

I think you are wrong, sorry. I think you have the (x-2) part correct, but you need to come up with a better binomial for the other two solutions. How about x^2-8x+17, I think that works. By the way, the solution to your binomial would be +4sqrt(i)and -4sqrt(i) which is definitely not the homework problem!

Answer 3

4+i and 4-i will give the following factor
(x-4-i)(x-4+i)
=x^2-4x+xi-4x+16-4i-xi+4i-i^2
=x^2-8x+17
so the poly is
(x-2)(x^2-8x+17)
=x(x^2-8x+17)-2(x^2-8x+17)
=x^3-8x^2+17x-2x^2+16x-34
=x^3-10x^2+33x-34

Answer 4

sorry dude u got it wrong when u multiply two complementary no like 4+i and 4-i you wont get an imaginary no

Answer 5

Excellent. That is the correct answer.

Answer 6

yes young lady that is perfect