Answer:
f(x) = x^3 -7x^2 +9x +17
Step-by-step explanation:
If the polynomial has real coefficients, then any complex roots come in conjugate pairs. Since 4-i is a root, 4+i is also a root. For each root r, the polynomial has a factor (x-r), so the minimal polynomial is ...
f(x) = (x -(-1))(x -(4-i))(x -(4+i))
= (x +1)((x -4)^2 -i^2) . . . . difference of squares
= (x +1)(x^2 -8x +17)
f(x) = x^3 -7x^2 +9x +17
