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Math Help - Polynomial Function

  1. #1
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    Polynomial Function

    For the polynomial function below, state the zeros and the multiplicity.

    f(x) = (x + sqrt{3})^2 (x - 2)^4

    What is the easiest way or method for finding the zeros of polynomial functions?
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  2. #2
    Moo
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    Quote Originally Posted by magentarita View Post
    For the polynomial function below, state the zeros and the multiplicity.

    f(x) = (x + sqrt{3})^2 (x - 2)^4

    What is the easiest way or method for finding the zeros of polynomial functions?
    To see its factorised form, like what you have.

    See my answer to your other thread : http://www.mathhelpforum.com/math-he...tiplicity.html

    Don't you have any textbook or teacher's notes ?

    You can look here too : Polynomial Graphs: Zeroes and Their Multiplicities (which I found by googling "polynomial multiplicity" )
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  3. #3
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    yes

    Quote Originally Posted by Moo View Post
    To see its factorised form, like what you have.

    See my answer to your other thread : http://www.mathhelpforum.com/math-he...tiplicity.html

    Don't you have any textbook or teacher's notes ?

    You can look here too : Polynomial Graphs: Zeroes and Their Multiplicities (which I found by googling "polynomial multiplicity" )
    Yes, I have the textbook and teacher's notes but if I understood that there would be no reason to post questions here.
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  4. #4
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    the root negetive root three has a multiplicity of 2
    the root two has a multiplicity of 4

    if you set each factor equal to zero and solve for x, that gives you the root from factored form

    the exponent that the factor is raised to is the multiplicity, because that is the number of times that that factor is a factor of the polynomial (maybe it's easier to understand if i show you an example:

    x(squared)-4x+4
    factors to (x-2)(x-2)
    which is the same as (x-2)squared

    the root is x-2=0 so x=2
    so the root x=2 has a multiplicity of 2 in my example)

    in your situation there is a root (x-2) raised to the 4th, so the root x=2 has a multiplicity of 4
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  5. #5
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    good..

    Quote Originally Posted by mikedwd View Post
    the root negetive root three has a multiplicity of 2
    the root two has a multiplicity of 4

    if you set each factor equal to zero and solve for x, that gives you the root from factored form

    the exponent that the factor is raised to is the multiplicity, because that is the number of times that that factor is a factor of the polynomial (maybe it's easier to understand if i show you an example:

    x(squared)-4x+4
    factors to (x-2)(x-2)
    which is the same as (x-2)squared

    the root is x-2=0 so x=2
    so the root x=2 has a multiplicity of 2 in my example)

    in your situation there is a root (x-2) raised to the 4th, so the root x=2 has a multiplicity of 4

    Good reply.

    Thanks
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