Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

haterofmath

  • one year ago

Find all rational zeros of the polynomial. P(x) = x^3 + 6x^2 − 32

  • This Question is Closed
  1. Stiwan
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    A good trick whenever you have to find rational zeroes of a polynomial is to try all factors of the term without an x (In this case 32). For example, try x = 2.

  2. Stiwan
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't know if you're aware of it, but every polynomial can be rewritten in the following form: \[a_n x^n + a_{n-1}x^{n-1} + ... + a_1 x + a_0 = (x - x_1) \cdot (x - x_2 ) *...*(x - x_n)\] where x_1, x_2, ..., x_n are the zeroes of the polynomial. Looking at these you can see that \[a_0 = x_1 * x_2 * ... * x_n\] Hence any rational zero of p(x) must be a factor of a_0. Also, if you have found a zero, let's call it x_1, you can divide your original polynomial by (x-x_1) and the zeroes of the resulting polynomial are the remaining ones of your original polynomial

  3. amoodarya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1357856688059:dw|

  4. amoodarya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1357856862910:dw|

  5. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.