A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
What are the possible number of positive, negative, and complex zeros of f(x) = –3x4 + 5x3 – x2 + 8x + 4 ?
anonymous
 4 years ago
What are the possible number of positive, negative, and complex zeros of f(x) = –3x4 + 5x3 – x2 + 8x + 4 ?

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It equals the highest degree of your polynomial.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0All zeros are complex, meaning they are of the form a+bi. Sometimes b=0, which eliminates the imaginary component, making it appear to be only real. So the number of complex roots of a polynomial is equal to the highest degree. I missed that you asked about positive and negative zeros. That would use Descartes' Rule of Signs as @shubhamsrg suggested.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Descarte's Rule says to count how many times the signs change from term to term in your polynomial. Then the number of positive zeros is either equal to that number or equal to that number minus even integers. I count 3 sign changes, so that would mean that there are either 3 or 32=1 positive real zeros.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The next step is to put a x into your polynomial everywhere there is an x. After you see how that negative would work out through the various powers, count the sign changes in this new f(x). The number of negative real zeros is equal that number or that number minus even integers. I counted 1. That would mean that there is 1 negative zero.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Since they asked for the possible numbers... I would say there are 3 positive real zeros possible, 1 negative real zero possible. And the number of complex roots is equal to the degree... do you know what that is?
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.