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4-2.Quadratic Equations and Inequations
hard
The number of distinct real roots of the equation $|\mathrm{x}+1||\mathrm{x}+3|-4|\mathrm{x}+2|+5=0$, is ...........
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
