f is an odd 5th degree polynomial with rational coefficients such that \(f({3- \sqrt{20} }) = 0\), \(f(0)=0\), and \(f(1)= -192\).
Give the rule for f.
So far, the only thing I know is that another root of x is \({ 3+ \sqrt{20} }\) based on conjugates and that the product of the roots has to be 0. If I could get a step by step walkthrough the process that would be great.
