Finding a polynomial function with given zeroes

To be exact, "Find a polynomial function with real coefficients that has the given zeros." My instructor just glazed over this in lecture and I don't see how the book is getting its answers. What exactly is the process to doing this? An example set of given zeros:

Re: Finding a polynomial function with given zeroes

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**zsf1990** To be exact, "Find a polynomial function with real coefficients that has the given zeros." My instructor just glazed over this in lecture and I don't see how the book is getting its answers. What exactly is the process to doing this? An example set of given zeros:

For your polynomial function to have real coefficients, all nonreal solutions will occur as complex conjugates. So you know that x = 4, x = -3i and x = 3i will all be zeroes of the polynomial. That means a polynomial that works is