4-2.Quadratic Equations and Inequations
hard

સમીકરણ $|\mathrm{x}+1||\mathrm{x}+3|-4|\mathrm{x}+2|+5=0$,નાં ભિન્ન વાસ્તવિક બીજોની સંખ્યા............ છે. 

A

$5$

B

$2$

C

$10$

D

$20$

(JEE MAIN-2024)

Solution

$|\mathrm{x}+1||\mathrm{x}+3|-4|\mathrm{x}+2|+5=0$

case $-1$

$ 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$

case $-2$

$ -3 \leq x \leq-2 $

$ -x^2-4 x-3+4 x+8+5=0 $

$ -x^2+10=0 $

$ x= \pm \sqrt{10}$

case $-3$

$ -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}$

case $-4$

$ x \geq-1 $

$ x^2+4 x+3-4 x-8+5=0 $

$ x^2=0 $

$ x=0$

No. of solution $=2$

Standard 11
Mathematics

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