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
College Algebra! help! -
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 - (-2-i) )
= (x^2 + 4x + 5)
so a possible polynomial is
f(x) = (x+4)(x^2 + 1)(x^2 + 4x + 5)
expand if needed