n=3; 4 and 5i are zeros; f(1)= -78

Answer 1

The complex conjugate of a complex zero is also a zero, so your zeros are

4

5i

-5i

f(x) = A(x - 4)(x - 5i)(x + 5i)

f(x) = A(x - 4)(x² + 25)

-78 = A(1 - 4)(1 + 25)

-78 = A(-3)(26)

A = 1

f(x) = (x - 4)(x² + 25)