Which of the following third-degree polynomial functions (with real coefficients)
has zeros at x=5+i and x=1?
Because we know that 5+i is a zero and the polynomial has to have real coefficients,
we know that the conjugate 5-i must also be a zero. So from the Linear Factorization
Theorem, f(x) can be written as
f(x)=a(x-1)(x-(5+i))(x-(5-i)); let’s take a=1 for simplicity’s sake