[tex]f(x)=x^3-5x^2+9x-5\\
f(x)=x^3-x^2-4x^2+4x+5x-5\\
f(x)=x^2(x-1)-4x(x-1)+5(x-1)\\
f(x)=(x-1)(x^2-4x+5)\\\\
(x-1)(x^2-4x+5)=0\\\\
x-1=0\\
x=1\\\\
x^2-4x+5=0\\
x^2-4x+4+1=0\\
(x-2)^2=-1\\
x-2=i \vee x-2=-i\\
x=2+i \vee x=2-i\\\\
x=\{1,2-i,2+i\}
[/tex]
