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Mathematics
The number of distinct real roots of the equation x 5( x 3- x 2- x +1)+ x (3 x 3-4 x 2-2 x +4)-1=0 text is
Q. The number of distinct real roots of the equation
x
5
(
x
3
−
x
2
−
x
+
1
)
+
x
(
3
x
3
−
4
x
2
−
2
x
+
4
)
−
1
=
0
is
407
135
JEE Main
JEE Main 2022
Complex Numbers and Quadratic Equations
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Answer:
3
Solution:
x
5
(
x
3
−
x
2
−
x
+
1
)
+
x
(
3
x
3
−
4
x
2
−
2
x
+
4
)
−
1
=
0
⇒
(
x
−
1
)
2
(
x
+
1
)
(
x
5
+
3
x
−
1
)
=
0
Let
f
(
x
)
=
x
5
+
3
x
−
1
f
′
(
x
)
>
0∀
x
∈
R
Hence
3
real distinct roots.