Algebra of Polynomials Questions | Prasnya
Prasnya
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Qualifier / Quiz 1
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Mathematics 1
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Week 4
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Algebra of Polynomials - Algebra of Polynomials
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Q1
Consider the polynomial
p
(
x
)
=
a
n
x
n
+
⋯
+
a
1
x
+
a
0
p(x)=a_nx^n+\cdots+a_1x+a_0
, where
a
i
∈
R
a_i \in \mathbb{R}
and
a
n
≠
0
a_n \ne 0
. Suppose
x
0
∈
R
x_0 \in \mathbb{R}
is the smallest root of
p
p
. From the options below, choose the conditions that ensure that
p
(
x
)
p(x)
is strictly decreasing in
(
−
∞
,
x
0
)
(-\infty,x_0)
.
Multiple correct
MARCH 15, 2026
MARCH 15, 2026
Q2
Consider two polynomials
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
p(x)=-x^5+5x^4-7x-2
and
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
q(x)=-x^5+5x^4-x^2-2
. Which of the following options is/are true?
Multiple correct
MARCH 15, 2026
MARCH 15, 2026
Q3
Consider the polynomial function
p
(
x
)
=
−
(
x
2
−
16
)
(
x
−
3
)
2
(
2
−
x
)
2
(
x
+
9
)
p(x)=-(x^2-16)(x-3)^2(2-x)^2(x+9)
. Choose the set correct options.
Multiple correct
MARCH 15, 2026
MARCH 15, 2026
