A) there is only one root
B) the sum of the roots is 1
C) the sum of the roots is 0
D) the product of the roots is 4
Correct Answer: C
Solution :
Given \[|x{{|}^{2}}+|x|-\,\,6=0\] Case I: \[x\ge 0\] Equation (i) reduces to\[{{x}^{2}}+x-6=0\] or \[(x+3)(x-2)=0\] or \[x=-3,\,\,2\] \[x=-3\] is impossible as\[x\ge 0\]. Therefore one root is\[x=2\]. Case II: \[x\le 0\] Equation (i) reduces to \[{{x}^{2}}-x-6=0\] or \[(x-3)(x+2)=0\] or \[x=3,\,\,-2\] \[x=3\] is impossible as\[x\le 0\]. Therefore one root is\[x=-2\]. Thus sum of the roots\[=0\].
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