Answer:
a. at -1 & 2
Step-by-step explanation:
The given function is
[tex]f(x)=x^4-2x^3+x-2[/tex].
Equate the function to zero.
[tex]x^4-2x^3+x-2=0[/tex].
Factor by grouping;
[tex]x^3(x-2)+1(x-2)=0[/tex]
Factor further;
[tex](x-2)(x^3+1)=0[/tex]
Apply the zero product property;
[tex](x-2)=0,(x^3+1)=0[/tex]
Solve for x;
[tex]x=2,x^3=-1[/tex]
[tex]\Rightarrow x=2,x=\sqrt[3]{-1}[/tex]
[tex]\therefore x=2,x=-1[/tex]
