• question_answer The product of all real roots of the equation ${{x}^{2}}-|x|-\,6=0$ is [Roorkee 2000] A) - 9 B) 6 C) 9 D) 36

Given equation ${{x}^{2}}-|x|-6=0$ If$x>0$, \ equation is ${{x}^{2}}-x-6=0$ Þ $(x-3)(x+2)=0$  Þ  $x=3,\,x=-2$  Þ $x=3$ If$x<0$,  \ equation is ${{x}^{2}}+x-6=0$ Þ $(x+3)(x-2)=0$ Þ  $x=-3,\,x=2$  Þ  $x=-3$ Hence product of all possible real roots = - 9.