EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
The parabola is
x
=
y
2
and
line equation is
x
=
0
. Find the quadratic equation.
(i)
2
y
2
=
0
(ii)
(
−
2
y
2
)
=
0
(iii)
y
2
=
0
(iv)
0
=
0
(v)
4
y
2
=
0
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
84
x
3
−
199
x
2
+
138
x
−
27
)
=
0
,
find
α + β + γ
(i)
(
−
199
84
)
(ii)
23
14
(iii)
(
−
23
14
)
(iv)
199
84
(v)
(
−
9
28
)
Question
3
3.
Factorize and divide
(
4
x
4
+
35
x
3
+
23
x
2
−
248
x
+
60
)
÷
(
−
x
2
−
4
x
+
12
)
(i)
(
−
4
x
2
−
19
x
+
5
)
(ii)
(
−
4
x
2
+
21
x
−
5
)
(iii)
(
−
4
x
2
+
19
x
+
5
)
(iv)
(
−
4
x
2
−
23
x
+
6
)
(v)
(
−
4
x
2
−
21
x
−
5
)
Question
4
4.
The sum of the roots of the quadratic equation
(
64
x
2
−
80
x
+
25
)
=
0
is
(i)
5
4
(ii)
7
6
(iii)
3
2
(iv)
7
4
(v)
3
4
Question
5
5.
The quotient when
(
−
4
d
2
+
8
d
)
is divided by
(
d
−
6
)
is
(i)
(
−
d
−
16
)
(ii)
(
−
4
d
−
16
)
(iii)
(
−
5
d
−
16
)
(iv)
(
−
7
d
−
16
)
(v)
(
−
3
d
−
16
)
Question
6
6.
The quotient when
(
−
s
)
is divided by
6
is
(i)
(
−
1
6
s
)
(ii)
1
6
s
(iii)
(
−
1
8
s
)
(iv)
(
−
1
2
s
)
(v)
(
−
1
4
s
)
Question
7
7.
Which of the following are true?
a)
The curve of a parabola
is a
curve
b)
The curve of a parabola
is a closed figure
c)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
always croses the X-axis
d)
The curve of a parabola
is a
circle
e)
The curve of a parabola
lie in only one quadrant
f)
The curve of a parabola
is a
straight line
(i)
{f,a}
(ii)
{d,e,a}
(iii)
{c,a}
(iv)
{a}
(v)
{b,a}
Question
8
8.
(
−
54
x
4
+
45
x
3
+
45
x
2
−
45
x
+
9
)
÷
(
27
x
3
−
9
x
2
−
27
x
+
9
)
=
(i)
(
−
x
+
1
)
(ii)
(
−
2
x
−
1
)
(iii)
(
−
2
x
+
1
)
(iv)
(
−
3
x
+
1
)
(v)
(
2
x
+
1
)
Question
9
9.
Which of the following equations represents the given graph ?
(i)
y
=
x
2
(ii)
y
=
2
x
2
(iii)
y
=
0
(iv)
y
=
4
x
2
(v)
y
=
3
x
2
Question
10
10.
Find the quadratic equation with roots
(
(
-2
7
)
,
(
-7
2
)
)
(i)
(
14
x
2
+
57
x
+
28
)
=
0
(ii)
(
14
x
2
+
53
x
+
14
)
=
0
(iii)
(
14
x
2
+
39
x
+
10
)
=
0
(iv)
(
10
x
2
+
39
x
+
14
)
=
0
(v)
(
28
x
2
+
57
x
+
14
)
=
0
Question
11
11.
Which of the following are true?
a)
A polynomial of degree n has atmost n zeros
b)
Zero of a polynomial and zero polynomial are synonymous
c)
If (x - a) is a factor of f(x), then f(a) = 0
d)
A linear polynomial in one variable has only one root
e)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
f)
Zero of a polynomial and root of the polynomial are synonymous
g)
If (x + a) is a factor of f(x), then f(a) = 0
(i)
{b,e,f}
(ii)
{b,a}
(iii)
{g,c}
(iv)
{a,c,d,e,f}
(v)
{b,g,d}
Question
12
12.
Which of the following polynomials is a multiple of
(
2
x
+
3
)
?
(i)
(
8
x
3
+
12
x
2
−
2
x
−
3
)
(ii)
(
4
x
3
+
4
x
2
−
x
−
1
)
(iii)
(
2
x
3
+
x
2
−
13
x
+
6
)
(iv)
(
2
x
3
−
x
2
−
5
x
−
2
)
(v)
(
x
3
+
2
x
2
−
5
x
−
6
)
Question
13
13.
Find the quadratic equation with roots
(
(
-3
5
)
,
(
-3
5
)
)
(i)
(
35
x
2
+
36
x
+
9
)
=
0
(ii)
(
25
x
2
+
30
x
+
9
)
=
0
(iii)
(
25
x
2
+
20
x
+
3
)
=
0
(iv)
(
5
x
2
+
8
x
+
3
)
=
0
Question
14
14.
Which of the following equations represents the given graph ?
(i)
y
=
(
2
x
2
−
4
x
−
6
)
(ii)
y
=
(
3
x
2
−
x
−
6
)
(iii)
y
=
(
2
x
2
+
2
x
−
6
)
(iv)
y
=
(
2
x
2
−
x
−
6
)
(v)
y
=
(
x
2
−
x
−
6
)
Question
15
15.
If
α
=
7
9
,
β
=
9
8
,
γ
=
8
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
(
−
329
72
)
(ii)
7
3
(iii)
(
−
7
3
)
(iv)
1285
216
(v)
(
−
1285
216
)
Question
16
16.
The degree of the polynomial
(
4
a
4
+
2
a
3
+
6
a
2
−
a
+
2
)
is
(i)
3
(ii)
4
(iii)
7
(iv)
2
(v)
5
Question
17
17.
Find the value of
k
such that
x
3
+
3
x
2
+
k
x
−
8
is exactly divisible by
(
x
+
1
)
(i)
-4
(ii)
-9
(iii)
-7
(iv)
-5
(v)
-6
Question
18
18.
If one of the roots of the cubic equation
(
x
3
+
13
x
2
+
34
x
−
48
)
=
0
is
1
,
find the remaining real roots
(i)
(
(
−
1
)
,
(
−
10
)
)
(ii)
(
2
,
(
−
7
)
)
(iii)
(
(
−
8
)
,
(
−
6
)
)
(iv)
(
0
,
(
−
9
)
)
(v)
(
3
,
(
−
6
)
)
Question
19
19.
If
α
=
1
6
,
β
=
3
2
,
γ
=
1
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
1
12
)
(ii)
29
36
(iii)
1
12
(iv)
(
−
29
36
)
(v)
(
−
2
)
Question
20
20.
Find the remainder when
(
2
x
2
−
8
x
−
42
)
is divided by
(
x
−
4
)
(i)
-39
(ii)
-41
(iii)
-45
(iv)
-42
(v)
-43
Question
21
21.
Find the table of points that satisfy
the parabola equation
y
=
(
−
4
x
2
)
(i)
x
-2
-1
0
1
2
y
-16
-4
0
-4
-16
(ii)
x
-2
-1
0
1
4
y
-16
-4
0
-4
-14
(iii)
x
-2
-1
0
0
2
y
-16
-4
0
-3
-16
(iv)
x
-2
-1
1
1
2
y
-16
-4
-1
-4
-16
(v)
x
-2
-1
-2
1
2
y
-16
-4
-2
-4
-16
Question
22
22.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
−
9
x
3
−
42
x
2
+
17
x
+
10
)
,
g
(
x
)
=
(
−
x
+
2
)
(ii)
f
(
x
)
=
(
−
3
x
3
+
26
x
2
−
52
x
+
24
)
,
g
(
x
)
=
(
x
+
5
)
(iii)
f
(
x
)
=
(
3
x
3
−
23
x
2
+
28
x
+
12
)
,
g
(
x
)
=
(
−
x
+
6
)
(iv)
f
(
x
)
=
(
−
3
x
3
−
22
x
2
−
29
x
+
30
)
,
g
(
x
)
=
(
3
x
+
1
)
(v)
f
(
x
)
=
(
3
x
3
+
7
x
2
−
36
x
+
20
)
,
g
(
x
)
=
(
x
+
3
)
Question
23
23.
Which of the following equations represents the given graph ?
(i)
x
=
(
−
3
y
2
)
(ii)
x
=
(
−
2
y
2
)
(iii)
x
=
(
−
5
y
2
)
(iv)
x
=
(
−
6
y
2
)
(v)
x
=
(
−
4
y
2
)
Question
24
24.
Find the quadratic equation, the sum of whose roots is
-6
and product is
9
(i)
(
x
2
+
9
x
+
9
)
=
0
(ii)
(
x
2
+
6
x
+
9
)
=
0
(iii)
(
6
x
+
9
)
=
0
(iv)
(
2
x
2
+
6
x
+
9
)
=
0
(v)
(
x
2
+
4
x
+
9
)
=
0
Question
25
25.
The sum of the roots of the quadratic equation
(
7
x
2
+
11
x
−
6
)
=
0
is
(i)
(
-9
7
)
(ii)
(
-13
7
)
(iii)
(
-9
5
)
(iv)
(
-13
9
)
(v)
(
-11
7
)
Assignment Key
1) (iii)
2) (iv)
3) (i)
4) (i)
5) (ii)
6) (i)
7) (iv)
8) (iii)
9) (ii)
10) (ii)
11) (iv)
12) (i)
13) (ii)
14) (iv)
15) (iv)
16) (ii)
17) (v)
18) (iii)
19) (v)
20) (iv)
21) (i)
22) (iii)
23) (v)
24) (ii)
25) (v)
