algebra question

Question

A polynomial function f(x) with real coefficients has the given degree, zeros, and solution point.

Degree		Zeros		Solution Point
4		−1, 5, i		f(1) = 48

Answer 1

THen -i is also a solution because the polynomial has real coefficients...

f(x) =

k(x+1)(x-5)(x-i)(x+i) =

k(x+1)(x-5)(x^2+1)

f(1) = 48 ---> (1,48)

48 = k(2)(-4)(2)

48 = -16*k

k = -3

f(x) = -3(x+1)(x-5)(x^2+1)