Form a polynomial whose real zeros and degree are given. ​Zeros: minus−11​, ​0, 55​; ​ degree: 3 Type a polynomial with integer coefficients

Question

Form a polynomial whose real zeros and degree are given. ​Zeros: minus−11​, ​0, 55​; ​ degree: 3 Type a polynomial with integer coefficients and a leading coefficient of 1.

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Isabelle 4 weeks 2021-09-21T15:01:30+00:00 1 Answer 0

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    2021-09-21T15:03:16+00:00

    Answer:

    Therefore,

    A polynomial with integer coefficients and a leading coefficient of 1,

    x^{3}-44x^{2}-605x=0

    Step-by-step explanation:

    Given:

    ​Zeros:

    −11​, ​0, 55​; ​

    degree: 3

    To Find:

    Type a polynomial with integer coefficients and a leading coefficient of 1.

    Solution:

    For a Polynomial degree will decide the number of zeros,

    Degree: n indicates “n” number of zeros.

    Here, degree: 3 indicates 3 zeros

    Let for a Polynomial of degree 3 and ZEROS: a , b and c. then the polynomial is given as

    P(x)=(x-a)(x-b)(x-c)=0

    Here Zeros are

    a = -11,

    b = 0,

    c = 55

    Therefore,

    P(x)=(x-(-11))(x-0)(x-55)=0\\\\(x+11)x(x-55)=0\\\\x(x^{2}-44x-605)=0\\\\x^{3}-44x^{2}-605x=0  …Which is the required Polynomial

    Therefore,

    A polynomial with integer coefficients and a leading coefficient of 1,

    x^{3}-44x^{2}-605x=0

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45:7+7-4:2-5:5*4+35:2 =? ( )