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JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Quadratic Equation

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

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

Correct answer

0

Step-by-step solution

Case I : x≥−5x \geq-5x2+5x+2x+12=0x2+7x+12=0x=−3,−4\begin{aligned} & x^2+5 x+2 x+12=0 \\ & x^2+7 x+12=0 \\ & x=-3,-4 \end{aligned}Case II : $-7 < \mathrm{x} < -5 -x^2-5 x+2 x+14-2=0\begin{aligned} & -x^2-3 x+12=0 \\ & x=\frac{-3 \pm \sqrt{9+48}}{2} \\ & =\frac{-3 \pm \sqrt{57}}{2} \\ & x=\frac{-3-\sqrt{57}}{2}, \frac{-3+\sqrt{57}}{2} \text{ (rejected) } \end{aligned}$ Case III : $\mathrm{x} \leq-7\begin{aligned} & -x^2-5 x-2 x-14-2=0 \\ & x^2+7 x+16=0 \\ & D=49-64 < 0 \end{aligned}$$NosolutionsNo.ofsolutionsNo solutions No. of solutions=3$
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