Find a polynomial f (x) of degree 4 with real coefficients and the following zeros.

-2 (multiplicity 2), i

F (X) = ?

f (x) = x^4 + 4x^3 + 5x^2 + 4x + 4

Step-by-step explanation:

If "a" is a zero, then (x-a) is a factor. The conjugate of a complex zero is also a zero if the polynomial has real coefficients. Then the factorization is ...

f (x) = (x - (-2)) (x - (-2)) (x - i) (x - (-i)) = (x^2 + 4x + 4) (x^2 + 1)

f (x) = x^4 + 4x^3 + 5x^2 + 4x + 4