Find a fourth-degree polynomial with integer coefficients that has zeros 4i and −1, with −1 a zero of multiplicity 2.

Question

Find a fourth-degree polynomial with integer coefficients that has zeros 4i and −1, with −1 a zero of multiplicity 2.

Answer 1

(x+1)^2(x^2+16)=

(x^2+2x+1)(x^2+16)=

x^4 + 2x^3 + 17x^2 + 32x +16 is a 4th degree polynomial with zeros 4i,-4i and -1

set each factor = 0

x+1 = 0

x=-1

x^2+16 = 0

x^2 =-16

x =4i or -4i