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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

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    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.
     
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