Question
Asked Mar 7, 2020
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Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the function and verify the real zeros and the given function value.
n=3
3 and 4i are zeros
f(-1)=-68
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Expert Answer

Step 1

We write the general form for a 3 degree polynomial function as,

Algebra homework question answer, step 1, image 1

From the data provided, since complex roots occur in pairs, 4i and -4i will be the two imaginary roots.

Algebra homework question answer, step 1, image 2

Subsitute in the expression for f(x).

Algebra homework question answer, step 1, image 3

Step 2

Substitute x=-1

Algebra homework question answer, step 2, image 1

 

 

 

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