EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
The product of the roots of the quadratic equation
(
x
2
−
5
x
+
6
)
=
0
is
(i)
6
(ii)
5
(iii)
9
(iv)
4
(v)
7
Question
2
2.
Find the quadratic equation with roots
(
(
-1
8
)
,
(
-1
8
)
)
(i)
(
80
x
2
+
18
x
+
1
)
=
0
(ii)
(
64
x
2
+
32
x
+
3
)
=
0
(iii)
(
64
x
2
−
1
)
=
0
(iv)
(
64
x
2
+
16
x
+
1
)
=
0
(v)
(
48
x
2
+
14
x
+
1
)
=
0
Question
3
3.
Which of the following is a factor of
(
x
5
+
y
3
z
)
?
(i)
no factors
(ii)
x
2
z
(iii)
y
3
z
(iv)
x
5
(v)
y
Question
4
4.
The axis and origin of the parabola
y
=
(
−
x
2
−
x
)
are
(i)
x
=
1
2
,
(
1
2
,
1
4
)
(ii)
x
=
(
−
1
4
)
,
(
(
-3
4
)
,
(
-1
2
)
)
(iii)
x
=
(
−
1
)
,
(
5
4
,
(
-1
2
)
)
(iv)
x
=
(
−
1
2
)
,
(
(
-1
2
)
,
1
4
)
Question
5
5.
Find the quadratic equation with roots
(
(
-2
9
)
,
(
-7
4
)
)
(i)
(
28
x
2
+
57
x
+
14
)
=
0
(ii)
(
36
x
2
+
79
x
+
28
)
=
0
(iii)
(
36
x
2
+
71
x
+
14
)
=
0
(iv)
(
54
x
2
+
75
x
+
14
)
=
0
(v)
(
36
x
2
+
53
x
+
10
)
=
0
Question
6
6.
Which of the following is not an irreducible factor of
(
x
2
y
+
x
y
2
+
x
y
)
?
(i)
x
(ii)
x
y
(iii)
y
(iv)
(
x
+
y
+
1
)
Question
7
7.
If
α, β, γ
are the roots of the cubic equation
(
294
x
3
−
763
x
2
+
551
x
−
72
)
=
0
,
find
α + β + γ
(i)
(
−
551
294
)
(ii)
(
−
109
42
)
(iii)
(
−
12
49
)
(iv)
12
49
(v)
109
42
Question
8
8.
If the polynomial
b
x
4
+
5
x
3
−
14
x
2
−
23
x
+
a
is divided by
(
x
−
2
)
,
it leaves a remainder
0
.
If it is divided by
(
x
−
1
)
,
it leaves a remainder
0
.
Find the value of
a
and
b
(i)
1
,
29
(ii)
30
,
2
(iii)
31
,
2
(iv)
3
,
31
(v)
30
,
3
Question
9
9.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
4
0
0
4
12
24
40
(i)
y
=
(
2
x
2
+
8
x
+
4
)
(ii)
y
=
(
3
x
2
+
6
x
+
4
)
(iii)
y
=
(
2
x
2
+
3
x
+
4
)
(iv)
y
=
(
x
2
+
6
x
+
4
)
(v)
y
=
(
2
x
2
+
6
x
+
4
)
Question
10
10.
Find the quadratic equation, the sum of whose roots is
-3
and product is
2
(i)
(
−
13
x
2
−
36
x
−
24
)
=
0
(ii)
(
−
12
x
2
−
36
x
−
24
)
=
0
(iii)
(
−
12
x
2
−
38
x
−
24
)
=
0
(iv)
(
−
12
x
2
−
33
x
−
24
)
=
0
(v)
(
−
11
x
2
−
36
x
−
24
)
=
0
Question
11
11.
(
896
x
4
y
3
z
3
+
112
x
4
y
3
z
2
+
16
x
3
y
2
z
3
)
÷
4
x
2
y
z
=
(i)
(
28
x
2
y
3
z
2
+
224
x
2
y
2
z
2
+
4
x
y
z
2
)
(ii)
(
224
x
2
y
2
z
2
+
28
x
y
3
z
+
4
x
y
z
2
)
(iii)
(
224
x
3
y
4
z
2
+
28
x
2
y
2
z
+
4
x
y
z
2
)
(iv)
(
224
x
2
y
2
z
2
+
28
x
2
y
2
z
+
4
x
y
z
2
)
(v)
(
224
x
3
y
3
z
2
+
28
x
2
y
2
z
+
4
x
y
z
2
)
Question
12
12.
Which of the following are not polynomials?
a)
64
x
2
b)
√x
c)
(
12
x
+
8
y
)
(
8
x
−
11
y
)
d)
(
96
x
2
−
68
x
y
−
88
y
2
)
e)
(
8
x
−
11
y
)
(i)
{e,a,b}
(ii)
{b,c}
(iii)
{d,c}
(iv)
{d,c,b}
(v)
{a,b}
Question
13
13.
From the following graph of
x = p(y)
, find the roots of
p(y)
(i)
-4, -3, -2 and -6
(ii)
-4, -3, 4 and 0
(iii)
-4, -3, -2 and 0
(iv)
-1, -3, -2 and 0
(v)
-4, 2, -2 and 0
Question
14
14.
Given
f
(
n
)
=
(
8
n
−
2
)
,
find
f
(
2
)
(i)
17
(ii)
12
(iii)
14
(iv)
13
(v)
15
Question
15
15.
The value of the polynomial
(
2
y
4
+
9
y
3
−
5
y
2
+
6
y
−
7
)
at
y
=
1
is
(i)
4
(ii)
8
(iii)
6
(iv)
5
(v)
2
Question
16
16.
From the following graph of
x = p(y)
, find the number of zeroes of
p(y)
(i)
3
(ii)
0
(iii)
(-3)
(iv)
(-1)
(v)
1
Question
17
17.
Which of the following are not polynomials?
a)
√x
b)
(
6
x
−
3
y
)
c)
16
x
2
d)
(
2
x
+
y
)
e)
16
x
2
+
1
16
x
2
(i)
{a,e}
(ii)
{b,a}
(iii)
{c,e}
(iv)
{c,e,a}
(v)
{d,b,a}
Question
18
18.
If
α
=
5
9
,
β
=
3
2
,
γ
=
1
8
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
157
144
(ii)
(
−
157
72
)
(iii)
157
72
(iv)
(
−
5
48
)
(v)
5
48
Question
19
19.
Which of the following equations represents the given graph ?
(i)
y
=
x
2
(ii)
y
=
0
(iii)
y
=
3
x
2
(iv)
y
=
4
x
2
(v)
y
=
2
x
2
Question
20
20.
The remainder when
(
−
9
d
2
)
is divided by
(
d
+
1
)
is
(i)
(
−
10
)
(ii)
(
−
9
)
(iii)
(
−
8
)
(iv)
(
−
12
)
(v)
(
−
7
)
Question
21
21.
The value of the polynomial
(
8
c
−
7
)
at
c
=
(-4)
is
(i)
-40
(ii)
-37
(iii)
-39
(iv)
-38
(v)
-41
Question
22
22.
The sum of the roots of the quadratic equation
(
x
2
−
2
x
−
24
)
=
0
is
(i)
1
(ii)
2
(iii)
4
(iv)
3
(v)
0
Question
23
23.
Given
f
(
r
)
=
(
−
r
2
+
4
r
−
2
)
,
find
f
(
5
)
(i)
-4
(ii)
-6
(iii)
-7
(iv)
-8
(v)
-9
Question
24
24.
Find the roots of the quadratic equation
(
x
2
−
4
x
+
4
)
=
0
(i)
no real roots
(ii)
(
5
,
2
)
(iii)
(
2
,
2
)
(iv)
(
3
,
3
)
(v)
(
3
,
2
)
Question
25
25.
The quotient when
(
5
r
−
3
)
is divided by
(
r
−
2
)
is
(i)
2
(ii)
6
(iii)
5
(iv)
4
(v)
7
Assignment Key
1) (i)
2) (iv)
3) (i)
4) (iv)
5) (iii)
6) (ii)
7) (v)
8) (ii)
9) (v)
10) (ii)
11) (iv)
12) (ii)
13) (iii)
14) (iii)
15) (iv)
16) (ii)
17) (i)
18) (ii)
19) (v)
20) (ii)
21) (iii)
22) (ii)
23) (iii)
24) (iii)
25) (iii)
