A) One and only one real number
B) Real with sum one
C) Real with sum zero
D) Real with product zero
Correct Answer: C
Solution :
When \[\operatorname{x}<0,\,\,\left| x \right|=-\,x\] \[\therefore \,\,Equation\,\,is\,\,\,{{x}^{2}}-x-6=0\,\,\,\Rightarrow \,\,x=-2,\,\,3\] \[\because \,\,\,x<0\] \[\therefore \,\,\,x=-2\] is the solution. When \[\operatorname{x}\ge 0,\,\,\left| x \right|\,\,=\,\,x\] \[\therefore \,\,Equation is\,\,{{x}^{2}}+x\,-6=0 \,\Rightarrow x=2,\,\,-\,3\] \[\because ~\,\,\,\,x>0,\] \[\therefore \,\,\,\,x=2\,\,is\,\,the\,\,solution,\] Hence \[\operatorname{x}= 2\], - 2 are the solutions and their sum is zero.
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