EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
If
1
is the zero of the polynomial
f
(
x
)
=
k
x
2
+
4
x
−
10
,
find
k
(i)
6
(ii)
5
(iii)
8
(iv)
3
(v)
7
Question
2
2.
(
36
x
3
y
3
z
3
+
432
x
3
y
2
z
3
+
144
x
2
y
3
z
3
)
÷
6
x
y
z
2
=
(i)
(
6
x
2
y
2
z
+
72
x
2
y
z
+
24
x
y
2
z
)
(ii)
(
6
x
3
y
4
z
+
72
x
2
y
z
+
24
x
y
2
z
)
(iii)
(
72
x
2
y
2
z
2
+
6
x
2
y
2
z
+
24
x
y
2
z
)
(iv)
(
6
x
2
y
2
z
+
72
x
y
2
z
)
(v)
(
6
x
3
y
3
z
+
72
x
2
y
z
+
24
x
y
2
z
)
Question
3
3.
Find the table of points that satisfy
the parabola equation
y
=
(
−
4
x
2
−
8
x
−
4
)
(i)
x
-2
-1
0
1
2
y
-4
0
-4
-16
-36
(ii)
x
-2
-1
-2
1
2
y
-4
0
-6
-16
-36
(iii)
x
-2
-1
0
1
4
y
-4
0
-4
-16
-34
(iv)
x
-2
-1
0
0
2
y
-4
0
-4
-15
-36
(v)
x
-2
-1
1
1
2
y
-4
0
-5
-16
-36
Question
4
4.
Find the roots of the quadratic equation
(
−
8
x
2
−
6
x
−
6
)
=
0
(i)
(
1
,
1
)
(ii)
no real roots
(iii)
(
1
,
0
)
(iv)
(
3
,
0
)
Question
5
5.
Which of the following algebraic expressions is a cubic polynomial?
(i)
(
9
k
5
+
9
k
3
−
3
k
2
−
5
k
−
7
)
(ii)
(
−
7
k
+
2
)
(iii)
(
−
3
)
(iv)
(
−
5
k
2
+
3
k
−
7
)
(v)
(
−
k
3
−
8
k
2
−
6
k
−
8
)
Question
6
6.
If
α
=
1
6
,
β
=
9
5
,
γ
=
7
6
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
7
20
)
(ii)
(
−
467
180
)
(iii)
7
20
(iv)
47
15
(v)
(
−
47
15
)
Question
7
7.
The constant term in polynomial
(
−
6
f
3
+
9
f
2
−
3
f
−
7
)
is
(i)
-5
(ii)
-7
(iii)
-6
(iv)
-8
(v)
-9
Question
8
8.
Which of the following are true?
a)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
always croses the X-axis
b)
The curve of a parabola
is a
curve
c)
The curve of a parabola
lie in only one quadrant
d)
The curve of a parabola
is a
straight line
e)
The curve of a parabola
is a closed figure
f)
The curve of a parabola
is a
circle
(i)
{c,b}
(ii)
{a,b}
(iii)
{d,e,b}
(iv)
{f,b}
(v)
{b}
Question
9
9.
From the following graph of
y = p(x)
, find the roots of
p(x)
(i)
-1, 0, 2 and 3
(ii)
5, 0, 2 and 3
(iii)
-1, 0, 2 and 1
(iv)
-1, 0, -5 and 3
(v)
-1, -8, 2 and 3
Question
10
10.
The sum of the roots of the quadratic equation
(
36
x
2
+
60
x
+
25
)
=
0
is
(i)
(
-7
3
)
(ii)
-3
(iii)
(
-5
3
)
(iv)
(
-7
5
)
(v)
-1
Question
11
11.
Which of the following are true for m > 0 and a > 0?
a)
The curve of a parabola
x
=
−
m
y
2
lies in the I & II quadrant
b)
The curve of a parabola
y
=
−
m
x
2
lies in the I & II quadrant
c)
The curve of a parabola
y
=
m
x
2
lies in the I & II quadrant
d)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
lies in the I & II quadrant
e)
The curve of a parabola
x
=
−
m
y
2
lies in the II & III quadrant
(i)
{b,e}
(ii)
{a,c}
(iii)
{c,e}
(iv)
{d,a,c}
(v)
{b,e,c}
Question
12
12.
The quotient when
(
8
s
−
2
)
is divided by
(
s
+
8
)
is
(i)
8
(ii)
9
(iii)
7
(iv)
11
(v)
6
Question
13
13.
Which of the following are true for the parabola
y
=
a
x
2
+
b
x
+
c
?
a)
If the curve does not meet the X-axis,
there are no real roots for
y
=
a
x
2
+
b
x
+
c
b)
If the curve meets the X-axis at only one point ,
b
2
−
4
a
c
>
0
c)
If the curve meets the X-axis at only one point ,
b
2
−
4
a
c
=
0
d)
If the curve meets the X-axis at two places, there are two distinct non-real roots.
e)
If the curve does not meet the X-axis ,
b
2
−
4
a
c
< 0
(i)
{b,d,e}
(ii)
{a,c,e}
(iii)
{b,a,c}
(iv)
{b,a}
(v)
{d,c}
Question
14
14.
The point
(
(
−
4
)
,
(
−
64
)
)
lies on which of the given parabolae?
(i)
y
=
(
−
4
x
2
−
2
x
−
4
)
(ii)
y
=
(
−
4
x
2
−
4
)
(iii)
y
=
(
−
4
x
2
)
(iv)
y
=
(
−
4
x
2
−
2
x
)
Question
15
15.
Which of the following are not polynomials?
a)
x
2
+
1
x
2
b)
(
x
−
5
y
)
c)
x
2
d)
√x
e)
(
x
+
3
y
)
(i)
{b,a}
(ii)
{c,d,a}
(iii)
{c,d}
(iv)
{e,b,a}
(v)
{a,d}
Question
16
16.
The product of the roots of the quadratic equation
(
x
2
−
18
x
+
81
)
=
0
is
(i)
82
(ii)
84
(iii)
81
(iv)
80
(v)
79
Question
17
17.
Which of the following equations represents the given graph ?
(i)
y
=
2
x
2
(ii)
y
=
4
x
2
(iii)
y
=
x
2
(iv)
y
=
(
−
2
x
2
)
(v)
y
=
0
Question
18
18.
Which of the following algebraic expressions is a binomial?
(i)
(
−
2
j
+
3
)
(ii)
(
7
j
4
−
7
j
3
+
6
j
2
−
2
j
+
1
)
(iii)
4
j
2
(iv)
(
6
j
2
+
9
j
−
2
)
(v)
(
−
2
j
4
−
9
j
3
+
3
j
2
+
4
j
+
2
)
Question
19
19.
From the graph, find the approximate values of '
x
' for which
y
=
4
(i)
-0.22
,
-4.28
(ii)
-1.72
,
-2.78
(iii)
-2.22
,
-2.28
(iv)
-0.72
,
-3.78
(v)
-1.22
,
-3.28
Question
20
20.
The remainder when
(
4
v
3
+
5
v
2
+
7
v
)
is divided by
(
v
+
8
)
is
(i)
(
−
1784
)
(ii)
(
−
1785
)
(iii)
(
−
1782
)
(iv)
(
−
1783
)
(v)
(
−
1786
)
Question
21
21.
The coefficient of term
s
2
in polynomial
(
7
s
4
−
3
s
3
−
9
s
2
−
4
s
+
3
)
is
(i)
-10
(ii)
-12
(iii)
-9
(iv)
-8
(v)
-6
Question
22
22.
Find the quadratic equation with roots
(
(
-7
4
)
,
(
-7
4
)
)
(i)
(
16
x
2
+
48
x
+
35
)
=
0
(ii)
(
16
x
2
+
64
x
+
63
)
=
0
(iii)
(
8
x
2
+
42
x
+
49
)
=
0
(iv)
(
16
x
2
+
56
x
+
49
)
=
0
(v)
(
24
x
2
+
70
x
+
49
)
=
0
Question
23
23.
Find the roots of the quadratic equation
(
x
2
−
2
x
−
3
)
=
0
(i)
(
7
,
-1
)
(ii)
(
3
,
-1
)
(iii)
(
4
,
0
)
(iv)
(
4
,
-1
)
(v)
no real roots
Question
24
24.
The quotient when
(
7
s
2
+
9
s
−
1
)
is divided by
(
s
+
4
)
is
(i)
(
7
s
−
19
)
(ii)
(
10
s
−
19
)
(iii)
(
4
s
−
19
)
(iv)
(
8
s
−
19
)
(v)
(
6
s
−
19
)
Question
25
25.
(
10
x
4
+
24
x
3
+
8
x
2
)
÷
(
2
x
2
+
4
x
)
(i)
(
4
x
2
+
2
x
)
(ii)
(
5
x
2
−
2
x
)
(iii)
(
5
x
2
+
2
x
)
(iv)
(
−
5
x
2
+
2
x
)
(v)
(
5
x
2
+
3
x
)
Assignment Key
1) (i)
2) (i)
3) (i)
4) (ii)
5) (v)
6) (i)
7) (ii)
8) (v)
9) (i)
10) (iii)
11) (iii)
12) (i)
13) (ii)
14) (iii)
15) (v)
16) (iii)
17) (iii)
18) (i)
19) (v)
20) (i)
21) (iii)
22) (iv)
23) (ii)
24) (i)
25) (iii)
