# SOLUTION: How do you find an nth-degree polynomial function with real coefficients satisfying the given conditions? n=3; 1 and 5i are zeros; f (-1)=-104

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 Click here to see ALL problems on Linear Algebra Question 316701: How do you find an nth-degree polynomial function with real coefficients satisfying the given conditions? n=3; 1 and 5i are zeros; f (-1)=-104Answer by solver91311(16868)   (Show Source): You can put this solution on YOUR website! Use the following facts: The Fundamental Theorem of Algebra, namely that every -th degree polynomial function has exactly zeros, counting all multiplicities. Complex roots ALWAYS come in conjugate pairs. That means that if is a zero, then is also a zero of the desired polynomial function. If is a zero of a polynomial function in , then is a factor of the polynomial. A family of polynomial functions of the form: all have the same zeros. So we know the following things: 1. The desired polynomial function has exactly 3 zeros. 2. The zeros are , , and . 3. The factors of the polynomial, including any possible common factor multiplier are: Multiply the factors: Since Hence and John