Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ajprincess Group Title

Please help:) Find the relation between \(\alpha\), \(\beta\), \(\gamma\) in the order that \(\alpha+\beta x+\gamma x^2\) may be expressible in one term in the factorial notation.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. perl Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    maybe you can google a similiar question, and i will reply

    • 2 years ago
  2. perl Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok this is not what i am use to, algebra. what are you studying? what book

    • 2 years ago
  3. perl Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    engineering mathematics by amit k awasthi

    • 2 years ago
  4. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm no. I am nt studying any particular book. this question was given to me by my lecturer.

    • 2 years ago
  5. perl Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what is a factorial polynomial, can you give me a definition

    • 2 years ago
  6. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    A factorial polynomial \(x^p\) is defined as \(x^p=x(x-h)(x-2h)--------------(x-(p-1)h)\) where p is a positive integer.

    • 2 years ago
  7. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so, here take p= 2, a+bx+cx^2=x(x-h) and find relation between a,b,c.

    • 2 years ago
  8. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but i am not sure...

    • 2 years ago
  9. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    p=2 to make factorial polynomial as quadratic

    • 2 years ago
  10. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    jst a sec. am workng on it

    • 2 years ago
  11. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I am nt sure if what I have done is right. a=0, b=-h and c=1. am I right @hartnn?

    • 2 years ago
  12. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but that doesn't give u relation between them.......

    • 2 years ago
  13. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ya i am greatly confused

    • 2 years ago
  14. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    When I googled my question i found this link. http://acadmedia.wku.edu/Zhuhadar/eBooks/0977858251-STATISTICAL.pdf page number 229. i am trying to understand it

    • 2 years ago
  15. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    • 2 years ago
    1 Attachment
  16. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Suppose \(\alpha+\beta x+\gamma x^2=(u+vx)^2\). This means \(u^2+2uvx+v^2x^2=\alpha+\beta x+\gamma x^2.\) Equating coefficients, we have that \(u^2=\alpha\), \(2uv=\beta\), and \(v^2=\gamma\). These three equations imply \(2\sqrt{\alpha\gamma}=\beta\).

    • 2 years ago
  17. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    OH. You're doing Knuth-esque math. Okay, one second.

    • 2 years ago
  18. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    The above answer is technically true, but it's not what the professor is looking for. I'll explain what he's doing in a moment . . .

    • 2 years ago
  19. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    It would appear your professor made a significant error. He's using what's called the rising factorial and incorrectly at that. (He or she, whoever.) The following is the definition of the notation \(a^{(n)}\): \[ a^{(n)}=a(a+1)(a+2)\cdots(a+n-1)=\prod_{1\le i\le n}\left(a+i-1\right).\] What your professor wants, I believe, is the following: Let \(\alpha+\beta x+\gamma x^2=(u+vx)^{(2)}\). Then, following the definition of the rising factorial, we have \[(u+vx)^{(2)}=\prod_{1 \le i \le 2}\left(u+vx+i-1\right)=(u+vx)(u+vx+1).\] Expanding that our, we get \[(u+vx)(u+vx+1)=u^2+uvx+u+uvx+v^2x^2+vx=u^2+u+2uvx+vx+v^2x^2.\] Since we have let \(\alpha+\beta x+\gamma x^2=(u+vx)^{(2)}\), we have that \(\alpha+\beta x+\gamma x^2=(u^2+u)+(2uv+v)x+v^2x^2.\) From this we can conclude (by "equating coefficients") \(\alpha=u^2+u\), \(\beta=2uv+v\), and \(\gamma=v^2\). To search for a relation between our three variables, substitue \(\pm \sqrt{\gamma}\) for \(v\): \(\beta=\pm2u\sqrt{\gamma}\pm\sqrt{\gamma}\). Solving this equation for \(u\), we see that \(u=\frac{\beta \pm \gamma}{\pm 2\sqrt{\gamma}}.\) Substitution of this into \(\alpha=u^2+u\) reveals \[\alpha=\frac{(\beta\pm \gamma)^2}{4\gamma}+\frac{\beta \pm \gamma}{\pm 2\sqrt{\gamma}},\] giving us the desired: a relation between \(\alpha, \beta\) and \(\gamma\).

    • 2 years ago
  20. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thank you soooo much for the explanation:)

    • 2 years ago
  21. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    is that way wrong? So which method should I use? Actually the answer I posted is not the answer my professor gave me. Actually she didnt give us any answer yet

    • 2 years ago
  22. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    I don't think the way was entirely wrong. It's just that the author misunderstood the definition of \(a^{(n)}\). You know what I mean?

    • 2 years ago
  23. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm no. sorry

    • 2 years ago
  24. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    When the writer of that post said \[(a+bx)^{(2)}=(a+bx)[a+b(x-1)],\] they were wrong and this messed up the entire problem. However, what they were _trying_ to do was right.

    • 2 years ago
  25. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Does that make things more clear?

    • 2 years ago
  26. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ya it is. thank u soooo much:)

    • 2 years ago
  27. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    You're welcome. But, I'd like to thank you for the interesting problem!

    • 2 years ago
  28. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Let me go ahead and recommend--if you're getting problems like this a lot--Donald E. Knuth's Concrete Mathematics. In there, there's all kinds of this craziness: falling factorials, rising factorials, ceiling functions, floor functions, summations, discrete calculus, etc. It seems to directly pertain to what you're doing, but I can't be certain.

    • 2 years ago
  29. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks a lott:)

    • 2 years ago
  30. Limitless Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    You're welcome! Have a wonderful weekend.

    • 2 years ago
  31. ajprincess Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks nd wish u the same:)

    • 2 years ago
    • Attachments:

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
  • 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.