Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
eunjii
Group Title
Find the 3rd polynomial with roots 3 and 2 + i
I know my roots are 3, 2 + i, 2  i, but I don't know how to start my equation. Can someone please show me the steps to solve this problem?
 one year ago
 one year ago
eunjii Group Title
Find the 3rd polynomial with roots 3 and 2 + i I know my roots are 3, 2 + i, 2  i, but I don't know how to start my equation. Can someone please show me the steps to solve this problem?
 one year ago
 one year ago

This Question is Open

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you are looking for a quadratic whose zeros are \(2+i\) and \(2i\) when you find that, you need to multiply it by \(x3\) for your final answer there are a few ways to find the quadratic
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
one way is to memorize the following, if \(a+bi\) is a zero of a quadratic with leading coefficient 1, the quadratic is \[x^22ax+(a^2+b^2)\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
another way, in case you don't feel like memorizing that one, is to start with \[x=2+i\] and work backwards: \[x=2+i\] \[x2=i\] \[(x2)^2=i^2\] \[x^24x+4=1\] \[x^24x+5=0\]so your quadratic is \(x^24x+5\)
 one year ago

eunjii Group TitleBest ResponseYou've already chosen the best response.0
sorry I asked my question wrong. . .it was "Find the 3rd degree polynomial with roots 3 and 2 + i"
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
a final and not so pretty way is to start with \[(x(2+i))(x(2i))\] and multiply out
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yes, that is what we are trying to do
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
first step, find the quadratic with zeros \(2+i\) and its conjugate \(2i\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
that will be \(x^24x+5\) no matter what method you use then your final answer will be \[(x3)(x^24x+5)\]
 one year ago

eunjii Group TitleBest ResponseYou've already chosen the best response.0
Thank you so much~<3 The explanation was very clear and helpful.
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.