JEE Main20257 Apr 2025Evening ShiftMathematicsQuadratic EquationActual

The number of real roots of the equation x | x -2|+3| x -3|+1=0 is :

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Correct answer

C. 1

Step-by-step solution

aligned & (I) x 2 & -x^2+2 x-3 x+9+1=0 & x^2+x-10=0 & x= -1+ 41 2 , -1- 41 2 & aligned aligned & (II) 2 x 3 & x^2-2 x-3 x+9+1=0 & x^2-5 x+10=0 & D 0 & (III) x 3 & x^2-2 x+3 x-9+2=0 & x^2+x-8=0 & x= -1+ 32 2 , -1- 32 2 & aligned 1 real roots

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