The sum of values of x satisfying the equation |x^2+4x+3|+2x+5=0 is

Answers (1)

Solution:    If  x^2+4x+3=(x+3)(x+1)geq 0,x in R -(-3,-1)     ......(1)

                   The given equation  becomes     x^2+6x+8=0

             Rightarrow                      x=-2,-4             .........(2).........(2)

             From  (1),(2)       Rightarrow                x=-4

           If    x^2+4x+3< 0,xin (-3,-1)          ........(3)

          The equation becomes       -(x^2+4x+3)+2x+5=0

                                                x^2+2x-2=0Rightarrow x=-1pm sqrt3       .........(4)

        From (3),(4)       Rightarrow           x=-1-sqrt3

      Sum of the roots =-4+(-1-sqrt3)=-5-sqrt3.

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