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Joint Entrance Examination
Mathematics
Quadratic Equations and Inequalities
Question 47
Question 47 of 157
Medium
MCQ
The number of distinct real roots of x4 - 4x + 1 = 0 is :
A
4
B
2
C
1
D
0
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Solutions · 1
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Official solution
f
(
x
)
=
x
4
−
4
x
+
1
=
0
f(x) = {x^4} - 4x + 1 = 0
f
(
x
)
=
x
4
−
4
x
+
1
=
0
f
′
(
x
)
=
4
x
3
−
4
f'(x) = 4{x^3} - 4
f
′
(
x
)
=
4
x
3
−
4
=
4
(
x
−
1
)
(
x
2
+
1
+
x
)
= 4(x - 1)({x^2} + 1 + x)
=
4
(
x
−
1
)
(
x
2
+
1
+
x
)
\[\Rightarrow\] Two solution
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