1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Polynomial Functions w/ zeros.

  1. Oct 14, 2006 #1
    Ok I have a probelm with find the polynoimal function which has these zeros:

    Zeros: 2, 4+sqrt.(5), 4-sqrt.(5)

    Find the polynomial equation with the given zeros.

    So far I know:

    y=(x-2)(x-(4+sqrt.(5))(x-(4-sqrt.(5))

    but is there any way I could make the factor (x-(4+sqrt.(5)) into a better one? For example:

    Zeros: -2,-1,0,1,2

    I did:
    y=x(x^2-1)(x^2-4)

    instead of y=x(x+2)(x+1)(x-1)(x-2)

    Thanks! :biggrin:
     
  2. jcsd
  3. Oct 15, 2006 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Not "the" polynomial function- "a" polynomial function. There are an infinite number of polynomial functions having these zeros.

    Yes, much as you did with -2, 2, and -1, 1 below: [itex](x-(4+\sqrt{5}))(x- (4-\sqrt{5}))= ((x-4)+\sqrt{5})((x-4)-\sqrt{5})= (x-4)^2- 5[/itex]
    [itex]= x^2- 8x+ 16- 5= x^2- 8x+ 11 [/itex]
    That is the monic polynomial of lowest degree having those roots.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook