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Math Help - real zeros of the polynomial function

  1. #1
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    real zeros of the polynomial function

    im studying for a test and I have this review sheet but im stuck on this problem and need help.

    find all real zeros of the polynomial function. Determine the multiplicity of each zero: -2(x^2)+50(x^4)+3(x^3)-75(x^5)

    i know some of it but i get stuck in the middle. Help please?
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  2. #2
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    Hey,


    Quote Originally Posted by hammerbox View Post
    im studying for a test and I have this review sheet but im stuck on this problem and need help.

    find all real zeros of the polynomial function. Determine the multiplicity of each zero: -2(x^2)+50(x^4)+3(x^3)-75(x^5)

    i know some of it but i get stuck in the middle. Help please?
    -2(x^2)+50(x^4)+3(x^3)-75(x^5)

    First:

    -2(x^2)+50(x^4)+3(x^3)-75(x^5)

    = x^2 [-2+50x^2+3x - 75x^3]

    = x^2 [-75x^3 + 50x^2 + 3x -2] = 0

    <=>x^2 = 0 \vee [-75x^3 + 50x^2 + 3x -2] = 0

    I guess you do not know how to solve [-75x^3 + 50x^2 + 3x -2] = 0

    Well, do you know Cardano's method or Newton's method to determine the zeros? If you don't I suggest you guess a zero, after that you use long polynomial division. So what methods do you know to find zeros?

    Solutions are:
    x1 = - 1/5
    x2 = 1/5
    x3 = 2/3
    x4,5 = 0

    Regards, Rapha
    Last edited by Rapha; December 18th 2008 at 05:51 PM.
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  3. #3
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    I haven't learned any of those methods nor long polynomial division in my class. Is there any other way to get the zeros other than those 3 ways?
    Last edited by hammerbox; December 18th 2008 at 06:10 PM.
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