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    Polynomials

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    Here is what the problem asks for:
    Give an example of a polynomial function f of degree 5 such that the only real roots of f(x) are -2,1,6 and
    f(2)=32. Show that your example works and leave f(x) in factored form.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:47 pm ad1c9bdddf
    https://brainmass.com/math/number-theory/polynomial-function-characteristic-examples-10846

    Solution Preview

    Since f(x) is of degree 5 and f(x) has three real roots -2,1,6, we can express f(x) as f(x)=(x+2)(x-1)(x-6)*g(x), where g(x) is a quadratic function.
    f(2)=32=(2+2)(2-1)(2-6)*g(2), so g(2)=-2
    We have two cases:
    Case 1: ...

    Solution Summary

    This shows how to give an example of a polynomial function with given characteristics.

    $2.19

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