A) 1
B) 2
C) 3
D) 4
Correct Answer: D
Solution :
Given equation : \[|x{{|}^{2}}-7|x|+12=0\] We know that \[|x{{|}^{2}}={{x}^{2}},\]so the given equation may be written as \[{{x}^{2}}-7|x|+12=0\] If \[x<0,\] \[{{x}^{2}}+7x+12=0\] \[[\because \,\,|x|=-x\,\,if\,\,x<0]\] \[\Rightarrow \,\,\,(x+4)\,\,(x+3)=0\] \[\Rightarrow \,\,\,x=-3,-4\] and, further If \[x>0\] \[{{x}^{2}}-7x+12=0\] \[[\because \,\,|x|=x,\,\,if\,x>0]\] \[\Rightarrow \,\,(x-4)\,(x-3)=0\Rightarrow x=3,4\] \[\therefore \] No. of roots = 4You need to login to perform this action.
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