Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.

Question

degree is 4

zeros are -3, 1, i

solution point is f(0)=-6

Answer 1

f(x) = a(x+3)(x-1)(x-i)(x+i)

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

f(0)=-6 = a(3)(-1)(1) = -3a

a =-6/-3 = 2

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

f(x) =2(x^4 +2x^3 -2x^2+2x-3)

f(x) = 2x^4 +4x^3 -4x^2 +4x -6