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Math Help - Polynomial of nth degree that includes zeroes

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    Polynomial of nth degree that includes zeroes

    Find a polynomial f(x) of degree 6 such that 0,3 are zeroes of multiplicity 3 and f(2) = -24. Write the polynomial in decreasing order of exponents.

    How do I do the above? What does it mean by zeroes of multiplicity 3???
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    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by mwok View Post
    Find a polynomial f(x) of degree 6 such that 0,3 are zeroes of multiplicity 3 and f(2) = -24. Write the polynomial in decreasing order of exponents.

    How do I do the above? What does it mean by zeroes of multiplicity 3???
    Multiplicity means the power it is raised to. So we have that

    f(x)=Ax^3(x-3)^3

    Now to find A we use our conditino

    -24=A(2)^3(-1)^3\Rightarrow{A=3}

    So your function is f(x)=3x^3(x-3)^3
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