Question

Need help I have a test tomorrow and I'm stuck on this extended response question. Can someone help me figure how to solve this problem?
A third-degree polynomial with rational coefficients has roots - 4 and - 4i. If the leading coefficient of the polynomial is 3 / 2, what is the polynomial?

Answer 1

Pretty sure I can do this, just give me a minute for me to do on it paper.

Answer 2

Ok thank you

Answer 3

Not 100% sure to be honest.

But normally, when given roots, to get back the equation. Just multiply out the roots.

An imaginary root will have it's conjugate as well.


(x+4)(x+4i)(x-4i)

Answer 4

Now you have to foil out the first two (it's easier), then the last one

Answer 5

Yep, just did it. That is how you do it.

Answer 6

Wanna try it yourself first?

Answer 7

Ok thanks @dtan5457

Answer 8

Just remember that i^2=-1

Other than that, this should be fairly simple

Answer 9

Ok I'm gonna see

Answer 10

Once your done, tell me your answer so I can check for you.

Answer 11

Ok

Answer 12

Ok when I foil do I multiply the x times 4i

Answer 13

Yes. It looks like a lot, but if you continue to multiply it out, all the random 4ix will cancel out.

Answer 14

\[x^3+4x^2+16x+64\]

That should be what you get.