Answer: The value of k =3.
Step-by-step explanation:
According to factor theorem, if g(x) =x-a is a factor of p(x) then p(a)=0.
Given: [tex]x-1[/tex] is a factor of [tex]k^2x^3-6kx+9[/tex].
then
[tex]k^2(1)^3-6k(1)+9=0\\\\\Rightarrow\ k^2-6k+9=0\\\\\Rightarrow\ k^2-3k-3k+9=0\\\\\Rightarrow\ k(k-3)-3(k-3)=0\\\\\Rightarrow\ (k-3)(k-3)=0\\\\\Rightarrow\ k=3[/tex]
Hence, the value of k =3.
