Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree​ 4; ​ zeros: −4−5i; 2 multiplicity 2

Answer 1

zeros: -4-5i and 2

x = -4 -5i

x+4 = -5i

x^2 + 8x + 16 = -25

x^2 + 8x + 41 = 0

x= 2

x-2 = 0

x^2 -4x + 4 = 0

the 4th degree polynomial is

(x^2 +8x + 41)(x^2 -4x + 4)

= x^4 +4x^3 + 13x^2- 132x + 164