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The number of distinct real roots of the equation |x+1||x+3|-4|x+2|+5=0 , is

Correct answer

2

Step-by-step solution

|x+1||x+3|-4|x+2|+5=0 case-1 aligned & x -3 & (x+1)(x+3)+4(x+2)+5=0 & x^2+4 x+3+4 x+8+5=0 & x^2+8 x+16=0 & (x+4)^2=0 & x=-4 aligned case-2 aligned & -3 x -2 & -x^2-4 x-3+4 x+8+5=0 & -x^2+10=0 & x= 10 aligned case-3 aligned & -2 x -1 & -x^2-4 x-3-4 x-8+5=0 & -x^2-8 x-6=0 & x^2+8 x+6=0 & x= -8 2 10 2 =-4 10 aligned case-4 aligned & x -1 & x^2+4 x+3-4 x-8+5=0 & x^2=0 & x=0 aligned No. of solution =2

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