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Math Help - State the multiplicity of each zero

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    State the multiplicity of each zero

    Find the zeros of the polynomial function and state the multiplicity of each zero:

    P(x)=x^2 (3 x+5)^2

    So I know that x=-5/3 but sense things are squared I'm loosing the picture.

    Is it 0 (multiplicity of 2) and -5/3 (multiplicity of 2)?
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  2. #2
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    Quote Originally Posted by RBlax View Post
    Is it 0 (multiplicity of 2) and -5/3 (multiplicity of 2)?
    Yup.
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    I honestly can just see it, but don't know the math that makes it true.

    How do I prove this?
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  4. #4
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    Quote Originally Posted by RBlax View Post
    I honestly can just see it, but don't know the math that makes it true.

    How do I prove this?
    You don't need to do any computation for this problem (other than solving 3x + 5 = 0), you just need to be able to apply the definition of multiplicity.

    Your book probably has a definition. Here is one definition:

    For a polynomial P(x) with root a, the multiplicity of a is the maximum integer k for which (x - a)^k divides P(x).

    If you wanted to, you could re-express P(x) given above as

    P(x)=9x^2\left(x-\left(-\frac{5}{3}\right)\right)^2
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