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Question 18 - Week 4 Practice | Prasnya
Q18
00:00
25 Feb 2024
Q18.
Consider two polynomials
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
p(x)=-x^5+5x^4-7x-2
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
and
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
q(x)=-x^5+5x^4-x^2-2
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
. Which of the following options is/are true?
A
q
(
x
)
→
∞
q(x)\to\infty
q
(
x
)
→
∞
as
x
→
∞
x\to\infty
x
→
∞
.
B
p
(
x
)
→
−
∞
p(x)\to-\infty
p
(
x
)
→
−
∞
as
x
→
∞
x\to\infty
x
→
∞
.
C
p
(
x
)
p(x)
p
(
x
)
has at most
4
4
4
turning points.
D
The quotient obtained while dividing
q
(
x
)
q(x)
q
(
x
)
by
p
(
x
)
p(x)
p
(
x
)
is a constant.
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Check
Details
Q18
00:00
25 Feb 2024
Q18.
Consider two polynomials
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
p(x)=-x^5+5x^4-7x-2
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
and
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
q(x)=-x^5+5x^4-x^2-2
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
. Which of the following options is/are true?
A
q
(
x
)
→
∞
q(x)\to\infty
q
(
x
)
→
∞
as
x
→
∞
x\to\infty
x
→
∞
.
B
p
(
x
)
→
−
∞
p(x)\to-\infty
p
(
x
)
→
−
∞
as
x
→
∞
x\to\infty
x
→
∞
.
C
p
(
x
)
p(x)
p
(
x
)
has at most
4
4
4
turning points.
D
The quotient obtained while dividing
q
(
x
)
q(x)
q
(
x
)
by
p
(
x
)
p(x)
p
(
x
)
is a constant.
Save
Check
Details
