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 \[{{\operatorname{x}}^{2}}-x-6=0 \Rightarrow \,\, x = -2,\,\,3\] \[\because \,\,\,\,\operatorname{x} < 0, \,\therefore x = -2\] is the solution. When \[\operatorname{x}\ge 0,\,\,\left| x \right|=x\] \[\therefore \,\,\,\operatorname{Equation} is {{x}^{2}} + x- 6 = 0 \Rightarrow x = 2, -3\] \[\because \,\,\,\,\operatorname{x} \ge 0, \,\therefore \,x= 2\] is the solution, Hence \[\operatorname{x} = 2, -2\] are the solutions and their sum is zero.
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