A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, 13, and 5 + 4i
A. f(x) = x4  8x3  12x2 + 400x  1599
B. f(x) = x4  200x2 + 800x  1599
C. f(x) = x4  98x2 + 800x  1599
D. f(x) = x4  8x3 + 12x2  400x + 1599
 2 years ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, 13, and 5 + 4i A. f(x) = x4  8x3  12x2 + 400x  1599 B. f(x) = x4  200x2 + 800x  1599 C. f(x) = x4  98x2 + 800x  1599 D. f(x) = x4  8x3 + 12x2  400x + 1599

This Question is Closed

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0Remember, to have zeros 3, 13 and 5+4i, f has factors x3, x+13 and x5+14i. Also if 5+4i is a zero, then 54i is also a zero. So at least f should look like: f(x)=(x3)(x+13)(x5+14i)(x514i). Now all you have to do is expand f to see which of A,B,C or D it is!

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0TYPO: read 4i and 4i instead of 14i ;)

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=expand+%28x3%29%28x%2B13%29%28x5%2B4i%29%28x54i%29

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0this part \((x(5+4i))(x(54i))\) can be a bit tricky. there are several ways to do it

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0one way is to work backwards: \[x=5+4i\] \[x5=4i\] \[(x5)^2=16\] \[x^210x+25=16\] \[x^210x+41\] is the quadratic

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0another way to to memorize that if the zeros are \(a+bi\) and \(abi\) then the quadratic with those zeros is \(x^22ax+a^2+b^2\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0you can then go right to \((x(5+4i))(x(54i))=x^210x+5^2+4^2\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0of course another way it to type it in to wolfram
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.