Question 1 - Roots, multiplicity, sign intervals and turning points Practice | Prasnya
Prasnya
Continue with Google
Practice path
Dashboard
Exam
Qualifier / Quiz 1
Go to subject
Mathematics 1
Go to chapter
Week 4
Go to topic
Graphs of Polynomials - Graphs of Polynomials
Go to subtopic
Roots, multiplicity, sign...
Question 1
00:00
Est. 3 min
Marks:
+5.00
0.00
Consider a polynomial function
p
(
x
)
=
−
0.01
(
x
−
1
)
(
x
−
2
)
2
(
x
−
3
)
2
(
x
−
4
)
x
(
x
+
1
)
(
x
+
2
)
2
p(x)=-0.01(x-1)(x-2)^2(x-3)^2(x-4)x(x+1)(x+2)^2
. Choose the correct options from the following.
Multiple correct
Hard Difficulty
05 June 2022
A
p
(
x
)
p(x)
is one-one function when
x
∈
(
−
∞
,
−
2
)
∪
(
4
,
∞
)
x\in(-\infty,-2)\cup(4,\infty)
.
B
The total number of turning points of
p
(
x
)
p(x)
is
9
9
.
C
p
(
x
)
>
0
p(x)>0
when
x
∈
(
−
1
,
0
)
∪
(
1
,
2
)
∪
(
2
,
3
)
∪
(
3
,
4
)
x\in(-1,0)\cup(1,2)\cup(2,3)\cup(3,4)
.
D
There are exactly
9
9
points on
p
(
x
)
p(x)
where the slope of the tangent is zero.
