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JEE Main 20248 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 8 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Quadratic Equation

JEE Main 2024 · 8 April · Evening Shift · Mathematics · Quadratic Equation

The number of distinct real roots of the equation...

The number of distinct real roots of the equation

|x+1||x+3|-4|x+2|+5=0

, is

Correct answer

2

Step-by-step solution

|x+1||x+3|-4|x+2|+5=0

case-1

\begin{aligned} & x \leq-3 \\ & (x+1)(x+3)+4(x+2)+5=0 \\ & x^2+4 x+3+4 x+8+5=0 \\ & x^2+8 x+16=0 \\ & (x+4)^2=0 \\ & x=-4 \end{aligned}

case-2

\begin{aligned} & -3 \leq x \leq-2 \\ & -x^2-4 x-3+4 x+8+5=0 \\ & -x^2+10=0 \\ & x= \pm \sqrt{10} \end{aligned}

case-3

\begin{aligned} & -2 \leq x \leq-1 \\ & -x^2-4 x-3-4 x-8+5=0 \\ & -x^2-8 x-6=0 \\ & x^2+8 x+6=0 \\ & x=\frac{-8 \pm 2 \sqrt{10}}{2}=-4 \pm \sqrt{10} \end{aligned}

case-4

\begin{aligned} & x \geq-1 \\ & x^2+4 x+3-4 x-8+5=0 \\ & x^2=0 \\ & x=0 \end{aligned}

No. of solution

=2

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