A) \[(-\infty ,0)\cup (2,\infty )\]
B) \[(-\infty ,1)\]
C) \[(0,1)\cup (2,\infty )\]
D) \[(1,2)\]
E) \[(0,2)\]
Correct Answer: C
Solution :
\[f(x)={{x}^{2}}{{(x-2)}^{2}}\] \[f(x)={{x}^{2}}.2(x-2)+2x.{{(x-2)}^{2}}\] \[=2x(x-2)(x+x-2)\] \[=4x(x-1)(x-2)\] The function is increasing. \[\Rightarrow \] \[f(x)>0\] \[4x(x-1)(x-2)>0\] \[\Rightarrow \] \[x\in (0,1)\cup (2,\infty )\]You need to login to perform this action.
You will be redirected in
3 sec