Questions: Write the polynomial f(x) that meets the given conditions. Answers may vary. Degree 3 polynomial with zeros of 4, 5i, and -5i. f(x)=

Write the polynomial f(x) that meets the given conditions. Answers may vary. Degree 3 polynomial with zeros of 4, 5i, and -5i. f(x)=
Transcript text: Write the polynomial $f(x)$ that meets the given conditions. Answers may vary. Degree 3 polynomial with zeros of $4,5 i$, and $-5 i$. \[ f(x)= \] $\square$
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Solution

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Solution Steps

Step 1: Identify the Zeros

The given zeros are: 4, 5j, (-0-5j).

Step 2: Form the Factors

The factors formed from the zeros are: (x - 4) * (x - (5j)) * (x - ((-0-5j))).

Step 3: Multiply the Factors

The multiplication of these factors forms the polynomial. For detailed steps, one would typically use polynomial multiplication techniques or a symbolic algebra system.

Step 4: Apply the Leading Coefficient

The leading coefficient is 1, so it does not change the polynomial.

Final Answer:

The polynomial is $f(x) = (x - 4)_(x - (5j))_(x - ((-0-5j)))$, where the multiplication of factors is not expanded for simplicity.

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