Answer:
[tex]f(x) = x^{3} - 5x^{2} + 7x - 3[/tex]
Step-by-step explanation:
If the polynomial has one root as 1 + i, it's conjugate 1 - i will also be its root.
Therefore, the polynomial has roots 1 + i, 1 - i, and 3.
So, the polynomial function of lowest degree with rational coefficients will be
f (x) = (x - 3)(x - 1 - i)(x - 1 + i)
⇒ [tex]f(x) = (x - 3)[ x^{2} - 2x + (1 + i)(1 - i)][/tex]
⇒[tex]f(x) = (x - 3)(x^{2} - 2x + 2)[/tex]
⇒ [tex]f(x) = x^{3} - 5x^{2} + 7x - 3[/tex] (Answer)
