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    Polynomial functions, complex zeros

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    1. Form a polynomial f(x) with real coefficents having the given degree and zeros
    Degree 5; Zeros: 2; -i; -7+i
    Enter the polynomial f(x)=a(____) type expression using x as the variable.

    2. Find a bound on the real zeros of the polynomial function.
    F(x)=x^4+x^3-4x-6
    Every real zero of f lies between -____and ____ (its not -2 and 2).

    3. Find the complex zeros of the polynomial function. Write f in factored form.
    F(x)=x^3-8x^2+29x-52
    Use the complex zeros to write f in factored form
    F(x)=____(reduce fractions and simplify roots)

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    https://brainmass.com/math/basic-algebra/polynomial-functions-complex-zeros-544351

    Solution Preview

    (please see the attached file for the complete solution)
    1. Form a polynomial f(x) with real coefficients having the given degree and zeros
    Degree 5; Zeros: 2; -i; -7+i
    Enter the polynomial f(x)=a(____) type expression using x as the variable

    Solution help:
    Note 1: Since the polynomial is of degree 5 than it can be factored into 5 factors of the
    form (x -a) where a is a zero
    i.e.
    (please see the attached file)

    Note 2: All complex zeros come as conjugate pairs
    i.e. if: (please see the attached file)
    .
    Based on the above:
    (please see the attached file)

    and:
    (please ...

    Solution Summary

    This solution involves finding a polynomial function based on its zeros and finding all the zeros of a given function.

    $2.19

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