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Joint Entrance Examination
Mathematics
Complex Numbers
Question 372
Question 372 of 455
Medium
MCQ
The number of real solutions of
x
2
−
3
∣
x
∣
+
2
=
0
x^2-3|x|+2=0
x
2
−
3∣
x
∣
+
2
=
0
is
A
3
B
2
C
4
D
1
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Official solution
∣
x
∣
2
−
3
∣
x
∣
+
2
=
0
⟹
(
∣
x
∣
−
2
)
(
∣
x
∣
−
1
)
=
0
⟹
∣
x
∣
=
1
,
2
⟹
x
=
±
1
,
±
2
|x|^2-3|x|+2=0 \implies (|x|-2)(|x|-1)=0 \implies |x|=1,2 \implies x=\pm1,\pm2
∣
x
∣
2
−
3∣
x
∣
+
2
=
0
⟹
(
∣
x
∣
−
2
)
(
∣
x
∣
−
1
)
=
0
⟹
∣
x
∣
=
1
,
2
⟹
x
=
±
1
,
±
2
. Number of solutions: 4.
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