Answer:
f(x) = x³ +20x² +16x +320
Explanation:
You want a third degree polynomial with zeros x = -20 and x = -4i, and a value of 1025 for x=5.
Factors
Each zero p means (x -p) is a factor. Each complex zero will correspond to another zero that is its conjugate. The give zeros mean the factored function is ...
f(x) = (x -(-20))(x -(-4i))(x -(4i)) = (x +20)(x² +16)
f(x) = x³ +20x² +16x +320
Check
To verify that f(5) = 1025, we can evaluate the function there:
f(5) = (5 +20)(5² +16) = 25(41) = 1025
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Additional comment
If we needed the value of f(5) to be something other than 1025, we could use the value of f(5) to find the appropriate scale factor. Here, we find the necessary scale factor is 1.
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