what is a cubic polynomial function with zeros 3,3 and -3? show your work.​

Question

what is a cubic polynomial function with zeros 3,3 and -3? show your work.​

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Gerda 4 months 2021-09-03T06:02:40+00:00 1 Answers 3 views 0

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    2021-09-03T06:04:00+00:00

    Answer:

    Cubic polynomial function with zeros 3,3 and -3 is \mathbf{x^3-3x^2-9x+27=0}

    Step-by-step explanation:

    We need to find a cubic polynomial function with zeros 3,3 and -3.

    If zeros of polynomial are: 3,3,and -3

    we can write:

    x=3, x=3, x=-3

    Or

    We can write:

    x-3=0, x-3=0, x+3=0

    Now, we can write them as:

    (x-3)(x-3)(x+3)=0

    Multiplying the terms, we can find the polynomial:

    (x-3)(x-3)(x+3)=0\\(x(x-3)-3(x-3))(x+3)=0\\(x^2-3x-3x+9)(x+3)=0\\(x^2-6x+9)(x+3)=0\\x(x^2-6x+9)+3(x^2-6x+9)=0\\x^3-6x^2+9x+3x^2-18x+27=0\\x^3-6x^2+3x^2+9x-18x+27=0\\x^3-3x^2-9x+27=0

    So, cubic polynomial function with zeros 3,3 and -3 is \mathbf{x^3-3x^2-9x+27=0}

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