The sum of the real roots of the equation $${x^2} + \left| x \right| - 6 = 0$$    is

Solution :
$$\eqalign{ & {\text{The given quadric equation is }}{x^2} + \left| x \right| - 6 = 0 \cr & {\text{Here, }}a = 1,{\text{ }}b = \pm 1{\text{ and }}c = - 6 \cr & {\text{As we know that }}D = {b^2} - 4ac \cr & {\text{Putting the value of }}a = 1,{\text{ }}b = \pm 1{\text{ and }}c = - 6 \cr & = {\left( { \pm 1} \right)^2} - 4 \times 1 \times - 6 \cr & = 1 + 24 \cr & = 25 \cr & {\text{Since, }}D \geqslant 0 \cr & {\text{Therefore, root of the given equation are real and distinct}}{\text{. }} \cr & {\text{Thus, sum of the roots be}} = 0. \cr} $$