JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 81

Cases. For $x\ge-5$ the equation needs $|x^2+3x+2|=-x-3\ge0$, i.e. $x\le-3$, where $x^2+3x+2>0$: $x^2+4x+5=0$, no real root. For $x<-5$: $x^2+3x+2=x+7$ gives $x=-1\pm\sqrt6$, neither below −5. No solutions.

Answer: 0