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Math Help - Finding roots of polynomial and zeros of multiplicity, is this correct?

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    Finding roots of polynomial and zeros of multiplicity, is this correct?

    Find roots of following polynomial and find zeroes of multiplicity.

    f(x) = 4x^5 + 12x^4 + 9x^3

    I got:
    f(x) = 4x^5 + 12x^4 + 9x^3 = 0
    x^3(4x^2 + 12x + 9) = 0
    x^3(2x + 3)(2x + 3) = 0


    x=0 OR x= -3/2
    Because (2x+3) occurs two times, the multiplicity of -3/2 is 2 and the multiplicity of 0 is 1

    Is it correct? Does it fully answer the question?
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    Quote Originally Posted by mwok View Post
    Find roots of following polynomial and find zeroes of multiplicity.

    f(x) = 4x^5 + 12x^4 + 9x^3

    I got:
    f(x) = 4x^5 + 12x^4 + 9x^3 = 0
    x^3(4x^2 + 12x + 9) = 0
    x^3(2x + 3)(2x + 3) = 0


    x=0 OR x= -3/2
    Because (2x+3) occurs two times, the multiplicity of -3/2 is 2 and the multiplicity of 0 is 1

    Is it correct? Does it fully answer the question?
    I would think so. This is my understanding of roots with multiplicity:

    If f(x) is a polynomial, and a is a root of f, then (x - a) is a factor of f(x).
    If (x - a) is a repeated factor, that is (x - a)^k is a factor of f(x), then a is a root with multiplicity k.
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