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Chapter 3: Theory of Equations
- Online Test
Chapter 3: Theory of Equations
TEST : 1
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q1.
A zero of
x
3
+
64 is
A.
0
B.
4
C.
4i
D.
-4
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q2.
If
f
and
g
are polynomials of degrees
m
and
n
respectively, and if
h
(
x
)
=
(
f
o
g
)
(
x
) , then the degree of
h
is
A.
mn
B.
m
+
n
C.
m
n
D.
n
m
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q3.
A polynomial equation in
x
of degree
n
always has
A.
n
distinct roots
B.
n
real roots
C.
n
imaginary roots
D.
at most one root.
View Solution
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Answer :
Option C
Explaination / Solution:
A polynomial of degree n always has n roots
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q4.
If
α
,
β
, and
γ
are the zeros of
x
3
+
px
2
+
qx
+
r
, then
is
A.
-
q
/
r
B.
-
p
/
r
C.
q
/
r
D.
-
q
/
p
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q5.
According to the rational root theorem, which number is not possible rational zero of
4
x
7
+
2
x
4
−
10
x
3
−
5 ?
A.
−1
B.
5/4
C.
4/5
D.
5
View Solution
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Answer :
Option B
Explaination / Solution:
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q6.
The polynomial
x
3
−
kx
2
+
9
x
has three real zeros if and only if,
k
satisfies
A.
|
k|
≤ 6
B.
k
= 0
C.
|
k|
> 6
D.
|
k|
≥ 6
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q7.
The number of real numbers in [0, 2
π
] satisfying sin
4
x
−
2 sin
2
x
+
1 is
A.
2
B.
4
C.
1
D.
∞
View Solution
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Answer :
Option A
Explaination / Solution:
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q8.
If
x
3
+
12
x
2
+
10
ax
+
1999 definitely has a positive zero, if and only if
A.
a ≥ 0
B.
a > 0
C.
a < 0
D.
a ≤ 0
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q9.
The polynomial
x
3
+
2
x
+
3 has
A.
one negative and two imaginary zeros
B.
one positive and two imaginary zeros
C.
three real zeros
D.
no zeros
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
TN State Board
TN 12th Standard
Maths
Chapter 3: Theory of Equations
Prepare / Learn
Q10.
The number of positive zeros of the polynomial
is
A.
0
B.
n
C.
<
n
D.
r
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
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Chapter 3: Theory of Equations
TEST : 1
Chapter 3: Theory of Equations
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TN State Board : TN 12th Standard (Maths)
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Chapter 1: Applications of Matrices and Determinants
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Chapter 2: Complex Numbers
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Chapter 3: Theory of Equations
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Chapter 4: Inverse Trigonometric Functions
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Chapter 5: Two Dimensional Analytical Geometry II
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Chapter 6: Applications of Vector Algebra
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