JEE Main20245 Apr 2024Evening ShiftMathematicsQuadratic EquationActual

The number of real solutions of the equation x|x+5|+2|x+7|-2=0 is_________

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Case I : x -5 aligned & x^2+5 x+2 x+12=0 & x^2+7 x+12=0 & x=-3,-4 aligned Case II : -7 < x < -5-x^2-5 x+2 x+14-2=0 aligned & -x^2-3 x+12=0 & x= -3 9+48 2 & = -3 57 2 & x= -3- 57 2 , -3+ 57 2 (rejected) aligned Case III : x -7 aligned & -x^2-5 x-2 x-14-2=0 & x^2+7 x+16=0 & D=49-64 < 0 aligned No solutions No. of solutions =3

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