Find a polynomial function of degree 7 with -2 as a zero of multiplicity​ 3, 0 as a zero of multiplicity3 ​, and 2 as a zero of multiplicity

Question

Find a polynomial function of degree 7 with -2 as a zero of multiplicity​ 3, 0 as a zero of multiplicity3 ​, and 2 as a zero of multiplicity 1.

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Mộc Miên 2 months 2021-08-28T18:16:52+00:00 1 Answers 0 views 0

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    2021-08-28T18:18:05+00:00

    Answer:

    The polynomial is p(x) = ax^3(x+2)^3(x-2), in which a is the leading coefficient.

    Step-by-step explanation:

    Zeros of a function:

    Given a polynomial f(x), this polynomial has roots x_{1}, x_{2}, x_{n} such that it can be written as: a(x - x_{1})*(x - x_{2})*...*(x-x_n), in which a is the leading coefficient.

    -2 as a zero of multiplicity​ 3

    This means that:

    p(x) = (x-(-2))^3 = (x+2)^3

    0 as a zero of multiplicity 3  

    Then also:

    p(x) = (x+2)^3(x-0)^3 = x^3(x+2)^3

    2 as a zero of multiplicity 1.

    Then:

    p(x) = x^3(x+2)^3(x-2)

    Adding the leading coefficient:

    p(x) = ax^3(x+2)^3(x-2)

    The polynomial is p(x) = ax^3(x+2)^3(x-2), in which a is the leading coefficient.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )