Question

Find the polynomial P(x) with interger coefficients that satisfy the following conditions:
P(x) has the degree 4 with zeros 3,0 and -i

Answer 1

x=3 => x-3 is a factor
x=0 => x-0 is a factor
x=-i => x-(-i) is a factor
x=i => x-i is a factor

P(x) has this form (x-a)(x-b)(x-c)(x-d) where a,b,c,d are the zeros
It has this form because it is 4th degree
Also since x=-i is a zero then x=i is one since we want real coefficients

Answer 2

Thanks it really helped alot