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

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day