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Question 5 - Week 4 Practice | Prasnya
Q5
00:00
26 Oct 2025
Q5.
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 5 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
Q5
00:00
26 Oct 2025
Q5.
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 5 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
