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JEE Main20245 Apr 2024Morning ShiftMathematicsFunctionsActual

The number of distinct real roots of the equation |x||x+2|-5|x+1|-1=0 is_______

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0

Step-by-step solution

Case-1 aligned & x 0 & x^2+2 x-5 x-5-1=0 & x^2-3 x-6=0 & x= 3 9+24 2 = 3 33 2 aligned One positive root Case-2 aligned & -1 x < 0 & -x^2-2 x-5 x-5-1=0 & x^2+7 x+6=0 & (x+6)(x+1)=0 & x=-1 aligned one root in range Case-3 aligned & -2 x < -1 & x^2-2 x+5 x+5-1=0 & x^2-3 x-4=0 & (x-4)(x+1)=0 aligned No root in range Case-4 aligned & x < -2 & x^2+7 x+4=0 & x= -7 49-16 2 = 7 33 2 aligned one root in range Total number of distinct roots are 3

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