The polynomial of degree 3 3 , P ( x ) P ( x ) , has a root of multiplicity 2 2 at x = 1 x = 1 and a root of multiplicity 1 1 at x = − 1 x =

Question

The polynomial of degree 3 3 , P ( x ) P ( x ) , has a root of multiplicity 2 2 at x = 1 x = 1 and a root of multiplicity 1 1 at x = − 1 x = – 1 . The y y -intercept is y = − 0.8 y = – 0.8 . Find a formula for P ( x ) P ( x ) . P ( x ) =

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Nho 5 months 2021-08-27T12:36:39+00:00 1 Answers 2 views 0

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    2021-08-27T12:37:49+00:00

    Answer:

    A formula for P(x) is;

    P(x) = -0.8·x³ + 0.8·x² + 0.8·x – 0.8

    Step-by-step explanation:

    The given parameters of the polynomial are;

    The degree of the polynomial = 3

    The multiplicity of the root at x = 1 is 2

    The multiplicity of the root at x = -1 is 1

    The y-intercept is y = -0.8

    Therefore, we have to find the formula for the three degree polynomial;

    The factors of the three degree polynomial are (x – 1)², and (x + 1)

    Multiplying the factors together, we get;

    (x – 1)²×(x + 1) = x³ – x² – x + 1

    f(0) = -0.8, therefore, we get;

    P(x) = -0.8 × (x – 1)² × (x + 1) = -0.8·x³ + 0.8·x² + 0.8·x – 0.8

    The required polynomial is;

    P(x) = -0.8·x³ + 0.8·x² + 0.8·x – 0.8

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