A) 0, 4
B) -1, 3
C) 4, 2
D) 5, 1
Correct Answer: A
Solution :
When \[x<2,\] \[{{(x-2)}^{2}}-(x-2)-6=0\] \[\Rightarrow {{x}^{2}}-4x+4-x+2-6=0\]\[\Rightarrow \] \[{{x}^{2}}-5x=0\] \[\Rightarrow \] \[x(x-5)=0\] \[\Rightarrow \] \[x=0\] When\[x\ge 2\]; \[{{(x-2)}^{2}}+(x-2)\,-6=0\] \[\Rightarrow {{x}^{2}}-4x+4+x-2-6=0\] \[\Rightarrow \] \[{{x}^{2}}-3x-4=0\] \[\Rightarrow \] \[{{x}^{2}}-4x+x-4=0\] \[\Rightarrow \] \[(x-4)(x+1)=0\] \[\Rightarrow \] \[x=4\].
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