A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Can someone help work through this problem with me :) f(x)= x^34x^2+16x64, zero 4i. Use the given zero to find the remaining zeros of f! I'm lost!
anonymous
 3 years ago
Can someone help work through this problem with me :) f(x)= x^34x^2+16x64, zero 4i. Use the given zero to find the remaining zeros of f! I'm lost!

This Question is Open

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0Rule #1 of complex roots: If you have one complex root, you have to have another corresponding one. In this example, since you have 4i as a zero, you also have to have 4i. In general, if you have a+bi as a root, you will also have abi as another root. Make sense so far?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0Great. So that means that \(x4i\) and \(x+4i\) both divide your polynomial. Notice that \((x4i)(x+4i)=x^24i+4i16i^2=x^2+16\) since \(i^2=1\).

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.0@KingGeorge is correct about the the roots in a case like this one, where the polynomial has rational coefficinets. In such a case, complex roots always come in complex conjugate pairs, a + bi and a  bi.

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0So \(x^2+16\) divides your polynomial. Can you try to find some factor \(x+a\) such that \((x+a)(x^2+16)=x^34x^2+16x64\)?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0Also, @mathstudent55 you just need real coefficients for it to work, not necessarily rational. But it should be noted that if your coefficients are complex numbers, that fact will not hold true.
Ask your own question
Sign UpFind more explanations on OpenStudy
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.