Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.

Question

n=3

2 and 5i are zeros

f(1)=26

Answer 1

then -5i is also a zero...

f(x) = k(x-2)(x-5i)(x+5i)

= k( x - 2)( x^2 + 25)

26 = k(-1)(26)

26 = k (-26)

k = -1

f(x) = - (x -2)(x^2 + 25)