Verified Solution • 2025–26 Session moderate QJEEM24Ma74ea: JEE Main 2024 Mathematics - Class 11 JEEM24Ma74ea Solution: The number of real solutions of the equation is __________. The number of real solutions of the equation x∣x+5∣+2∣x+7∣−2=0x|x+5|+2|x+7|-2=0x∣x+5∣+2∣x+7∣−2=0 is __________. Step-by-Step Verified Solution x∣x+5∣+2∣x+7∣−2=0x|x+5|+2|x+7|-2=0x∣x+5∣+2∣x+7∣−2=0 amp; (i) dx≥−5⇒x(x+5)+2(x+7)−2=0amp;x2+7x+12=0⇒x=−3,−4\begin{aligned}& \text { (i) } d x \geq-5 \Rightarrow x(x+5)+2(x+7)-2=0 \\& x^2+7 x+12=0 \Rightarrow x=-3,-4\end{aligned}amp; (i) dx≥−5⇒x(x+5)+2(x+7)−2=0amp;x2+7x+12=0⇒x=−3,−4 (ii)amp;x∈(−7,−5)amp;x(−x−5)+2(x+7)−2=0amp;−x2−3x+12=0amp;⇒x2+3x−12=0amp;⇒x=−3−572 satisfy \begin{aligned}\text{(ii)} \quad & x \in(-7,-5) \\& x(-x-5)+2(x+7)-2=0 \\& -x^2-3 x+12=0 \\& \Rightarrow x^2+3 x-12=0 \\& \Rightarrow x=\frac{-3-\sqrt{57}}{2} \text { satisfy }\end{aligned}(ii)amp;x∈(−7,−5)amp;x(−x−5)+2(x+7)−2=0amp;−x2−3x+12=0amp;⇒x2+3x−12=0amp;⇒x=2−3−57 satisfy (iii)amp;x≤−7amp;⇒x(−x−5)+2(−x−7)−2=0amp;−x2−7x−16=0⇒x2+7x+16=0\begin{aligned}\text{(iii)} \quad & x \leq-7 \\& \Rightarrow x(-x-5)+2(-x-7)-2=0 \\& -x^2-7 x-16=0 \Rightarrow x^2+7 x+16=0\end{aligned}(iii)amp;x≤−7amp;⇒x(−x−5)+2(−x−7)−2=0amp;−x2−7x−16=0⇒x2+7x+16=0 No solution Related Learning Resources & Exam Preparation JEE Main PYQ Question Bank Browse year-wise authentic previous years' questions with solutions Authentic CBT Mock Tests Simulate official exam environment with live timer and percentile scoring
