College Algebra! help!
posted by Hailey on .
Form a polynomial f(x) with the real coefficients having the given degree and zeros.
Degree 5; Zeros: 4; i; 2+i
f(x)=a( )

complex zeros always come in conjugate pairs
so if i is a zero , so is +i
if 2+i is a zero, so is 2  i
the zero of 4 comes from the factor (x+4)
the zeros of ±i come from (x^ + 1)
the zeros of 2 ± i produce
(x(2+i))(x  (2i) )
= (x^2 + 4x + 5)
so a possible polynomial is
f(x) = (x+4)(x^2 + 1)(x^2 + 4x + 5)
expand if needed