EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
If
2
and
-1
are the zeros of the polynomial
f
(
x
)
=
2
x
4
+
b
x
3
+
a
x
2
+
8
x
+
32
, find the value of
a
and
b
(i)
3
,
-23
(ii)
-24
,
3
(iii)
1
,
-25
(iv)
-24
,
2
(v)
-23
,
2
Question
2
2.
Which of the following algebraic expressions is a linear polynomial?
(i)
8
(ii)
(
7
d
5
−
2
d
4
−
2
d
2
−
7
d
+
7
)
(iii)
(
3
d
3
−
7
d
2
−
6
d
−
3
)
(iv)
(
7
d
2
+
4
d
+
9
)
(v)
(
−
2
d
−
2
)
Question
3
3.
(
18
x
4
−
39
x
3
−
6
x
2
+
21
x
+
6
)
÷
(
9
x
3
−
24
x
2
+
9
x
+
6
)
=
(i)
(
3
x
+
1
)
(ii)
(
x
+
1
)
(iii)
(
−
2
x
+
1
)
(iv)
(
2
x
−
1
)
(v)
(
2
x
+
1
)
Question
4
4.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
+
5
x
+
15
,
find the value of
a
(i)
0
(ii)
(-3)
(iii)
(-5)
(iv)
(-4)
(v)
(-2)
Question
5
5.
Which of the following equations represents the given graph ?
(i)
y
=
(
x
2
+
12
x
+
10
)
(ii)
y
=
(
2
x
2
+
12
x
+
10
)
(iii)
y
=
(
2
x
2
+
9
x
+
10
)
(iv)
y
=
(
2
x
2
+
14
x
+
10
)
(v)
y
=
(
3
x
2
+
12
x
+
10
)
Question
6
6.
The degree of the polynomial
(
−
9
f
5
+
3
f
4
+
4
f
3
+
3
f
−
8
)
is
(i)
3
(ii)
7
(iii)
4
(iv)
5
(v)
6
Question
7
7.
Which of the following equations represents the given graph ?
(i)
x
=
(
−
6
y
2
−
15
y
−
9
)
(ii)
x
=
(
−
6
y
2
−
18
y
−
9
)
(iii)
x
=
(
−
7
y
2
−
15
y
−
9
)
(iv)
x
=
(
−
5
y
2
−
15
y
−
9
)
(v)
x
=
(
−
6
y
2
−
13
y
−
9
)
Question
8
8.
Find the roots of the quadratic equation
(
x
2
−
10
x
+
25
)
=
0
(i)
(
6
,
5
)
(ii)
(
7
,
2
)
(iii)
(
6
,
4
)
(iv)
(
5
,
5
)
(v)
(
7
,
4
)
Question
9
9.
Find the value of
k
such that
8
x
3
−
20
x
2
+
k
x
+
125
is exactly divisible by
(
2
x
−
5
)
(i)
-47
(ii)
-50
(iii)
-52
(iv)
-49
(v)
-51
Question
10
10.
The quotient when
(
−
5
u
5
+
7
u
4
+
u
3
−
2
u
2
−
5
u
+
9
)
is divided by
(
u
−
2
)
is
(i)
(
−
2
u
4
−
3
u
3
−
5
u
2
−
12
u
−
29
)
(ii)
(
−
6
u
4
−
3
u
3
−
5
u
2
−
12
u
−
29
)
(iii)
(
−
8
u
4
−
3
u
3
−
5
u
2
−
12
u
−
29
)
(iv)
(
−
4
u
4
−
3
u
3
−
5
u
2
−
12
u
−
29
)
(v)
(
−
5
u
4
−
3
u
3
−
5
u
2
−
12
u
−
29
)
Question
11
11.
Find the table of points that satisfy
the parabola equation
y
=
(
−
9
x
2
)
(i)
x
-2
-1
0
1
4
y
-36
-9
0
-9
-34
(ii)
x
-2
-1
1
1
2
y
-36
-9
-1
-9
-36
(iii)
x
-2
-1
0
0
2
y
-36
-9
0
-8
-36
(iv)
x
-2
-1
0
1
2
y
-36
-9
0
-9
-36
(v)
x
-2
-1
-2
1
2
y
-36
-9
-2
-9
-36
Question
12
12.
If the polynomial
a
x
2
+
11
x
+
b
is divided by
(
x
−
5
)
,
it leaves a remainder
117
.
If it is divided by
(
3
x
−
1
)
,
it leaves a remainder
15
8
9
.
Find the value of
a
and
b
(i)
2
,
13
(ii)
11
,
1
(iii)
13
,
3
(iv)
3
,
12
(v)
2
,
12
Question
13
13.
The degree of the polynomial
(
−
5
b
4
−
b
2
−
5
)
is
(i)
2
(ii)
3
(iii)
5
(iv)
6
(v)
4
Question
14
14.
Which of the following algebraic expressions is a quadratic polynomial?
(i)
(
−
6
e
3
+
2
e
2
+
7
e
+
8
)
(ii)
(
−
2
e
−
3
)
(iii)
(
9
e
5
−
3
e
3
−
e
2
+
5
e
−
2
)
(iv)
6
(v)
(
4
e
2
−
6
e
−
3
)
Question
15
15.
Factorize and divide
(
9
x
4
−
148
x
2
+
64
)
÷
(
3
x
2
−
10
x
−
8
)
(i)
(
5
x
2
+
10
x
−
8
)
(ii)
(
10
x
−
8
)
(iii)
(
4
x
2
+
10
x
−
8
)
(iv)
(
2
x
2
+
10
x
−
8
)
(v)
(
3
x
2
+
10
x
−
8
)
Question
16
16.
The sum of the roots of the quadratic equation
49
x
2
=
0
is
(i)
3
(ii)
-1
(iii)
0
(iv)
1
(v)
-2
Question
17
17.
If
α
=
5
9
,
β
=
2
5
,
γ
=
5
9
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
10
81
)
(ii)
10
81
(iii)
68
45
(iv)
(
−
61
81
)
(v)
61
81
Question
18
18.
Which of the following are not polynomials?
a)
121
x
2
b)
(
6
x
−
8
y
)
c)
√x
d)
121
x
2
+
1
121
x
2
e)
(
6
x
+
10
y
)
(i)
{b,d}
(ii)
{e,a,c}
(iii)
{c,d}
(iv)
{a,c}
(v)
{b,d,c}
Question
19
19.
Find the quadratic equation, the sum of whose roots is
-12
and product is
36
(i)
(
2
x
2
+
12
x
+
36
)
=
0
(ii)
(
x
2
+
14
x
+
36
)
=
0
(iii)
(
12
x
+
36
)
=
0
(iv)
(
x
2
+
9
x
+
36
)
=
0
(v)
(
x
2
+
12
x
+
36
)
=
0
Question
20
20.
Find the quadratic equation with roots
(
1
2
,
(
-9
5
)
)
(i)
(
5
x
2
+
4
x
−
9
)
=
0
(ii)
(
14
x
2
+
11
x
−
9
)
=
0
(iii)
(
10
x
2
+
23
x
+
9
)
=
0
(iv)
(
10
x
2
+
9
x
−
7
)
=
0
(v)
(
10
x
2
+
13
x
−
9
)
=
0
Question
21
21.
Which of the displayed parabolae represents
the equation
y
=
(
8
x
2
+
5
)
(i)
parabola with point
J
(ii)
parabola with point
H
(iii)
parabola with point
I
(iv)
parabola with point
K
Question
22
22.
Find the table of points that satisfy
the parabola equation
y
=
x
2
(i)
x
-2
-1
0
1
2
y
4
1
0
1
4
(ii)
x
-2
-1
0
1
4
y
4
1
0
1
6
(iii)
x
-2
-1
1
1
2
y
4
1
-1
1
4
(iv)
x
-2
-1
0
0
2
y
4
1
0
2
4
(v)
x
-2
-1
-2
1
2
y
4
1
-2
1
4
Question
23
23.
The quotient when
(
−
7
i
2
)
is divided by
(
i
−
9
)
is
(i)
(
−
8
i
−
63
)
(ii)
(
−
9
i
−
63
)
(iii)
(
−
7
i
−
63
)
(iv)
(
−
5
i
−
63
)
(v)
(
−
6
i
−
63
)
Question
24
24.
If
α
=
1
7
,
β
=
5
8
,
γ
=
2
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
101
168
(ii)
(
−
241
168
)
(iii)
241
168
(iv)
(
−
5
84
)
(v)
(
−
101
168
)
Question
25
25.
Which of the following polynomials has
(
3
x
+
5
)
as a factor ?
(i)
(
12
x
3
+
12
x
2
−
75
x
−
75
)
(ii)
(
6
x
3
+
15
x
2
−
6
x
−
15
)
(iii)
(
9
x
3
+
9
x
2
−
9
x
−
9
)
(iv)
(
4
x
3
+
4
x
2
−
25
x
−
25
)
(v)
(
18
x
3
+
3
x
2
−
90
x
−
75
)
Assignment Key
1) (iv)
2) (v)
3) (v)
4) (ii)
5) (ii)
6) (iv)
7) (i)
8) (iv)
9) (ii)
10) (v)
11) (iv)
12) (v)
13) (v)
14) (v)
15) (v)
16) (iii)
17) (i)
18) (iii)
19) (v)
20) (v)
21) (iii)
22) (i)
23) (iii)
24) (ii)
25) (v)
