4. The roots of the equation
$$x ^ { 3 } - 4 x ^ { 2 } + 14 x - 20 = 0$$
are denoted by \(\alpha , \beta , \gamma\).
- Show that
$$\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = - 12$$
Explain why this result shows that exactly one of the roots of the above cubic equation is real.
- Given that one of the roots is \(1 + 3 \mathrm { i }\), find the other two roots. Explain your method for each root.