EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The sum of the roots of the quadratic equation
(
x
2
−
5
x
−
14
)
=
0
is
(i)
7
(ii)
4
(iii)
6
(iv)
5
(v)
3
Question
2
2.
If one of the roots of the cubic equation
(
x
3
+
3
x
2
−
13
x
−
15
)
=
0
is
(
−
1
)
,
find the remaining real roots
(i)
(
1
,
(
−
3
)
)
(ii)
(
(
−
4
)
,
(
−
7
)
)
(iii)
(
(
−
5
)
,
3
)
(iv)
(
(
−
2
)
,
(
−
6
)
)
(v)
(
0
,
(
−
4
)
)
Question
3
3.
Find the quadratic equation, the sum of whose roots is
-14
and product is
49
(i)
(
2
x
2
+
14
x
+
49
)
=
0
(ii)
(
x
2
+
12
x
+
49
)
=
0
(iii)
(
x
2
+
14
x
+
49
)
=
0
(iv)
(
14
x
+
49
)
=
0
(v)
(
x
2
+
16
x
+
49
)
=
0
Question
4
4.
The product of the roots of the quadratic equation
(
−
9
x
2
+
67
x
+
40
)
=
0
is
(i)
(
-38
9
)
(ii)
(
-32
7
)
(iii)
(
-48
11
)
(iv)
(
-40
9
)
(v)
(
-14
3
)
Question
5
5.
The quotient when
(
−
7
w
2
+
w
)
is divided by
(
w
−
2
)
is
(i)
(
−
10
w
−
13
)
(ii)
(
−
7
w
−
13
)
(iii)
(
−
6
w
−
13
)
(iv)
(
−
8
w
−
13
)
(v)
(
−
5
w
−
13
)
Question
6
6.
From the graph, find the approximate values of '
x
' for which
y
=
6
(i)
1.95
,
-1.95
(ii)
1.45
,
-1.45
(iii)
2.95
,
-2.95
(iv)
2.45
,
-2.45
(v)
3.45
,
-3.45
Question
7
7.
The given table of points satisfy which parabola equation?
x
9
4
1
0
1
4
9
y
-3
-2
-1
0
1
2
3
(i)
x
=
4
y
2
(ii)
x
=
y
2
(iii)
x
=
(
−
y
2
)
(iv)
x
=
0
(v)
x
=
2
y
2
Question
8
8.
Find the quadratic equation, the sum of whose roots is
(
-1
7
)
and product is
(
-8
7
)
(i)
(
42
x
2
+
6
x
−
48
)
=
0
(ii)
(
43
x
2
+
6
x
−
48
)
=
0
(iii)
(
42
x
2
+
8
x
−
48
)
=
0
(iv)
(
42
x
2
+
3
x
−
48
)
=
0
(v)
(
41
x
2
+
6
x
−
48
)
=
0
Question
9
9.
From the graph, find the approximate values of '
x
' for which
y
=
7
(i)
0.44
,
-3.44
(ii)
-0.06
,
-2.94
(iii)
-0.56
,
-2.44
(iv)
0.94
,
-3.94
(v)
1.44
,
-4.44
Question
10
10.
The value of the polynomial
0
at
c
=
4
,
d
=
5
,
e
=
4
is
(i)
-1
(ii)
0
(iii)
1
(iv)
2
(v)
-2
Question
11
11.
From the graph, find the approximate values of '
x
' for which
y
=
-4
(i)
-1.00
,
1.00
(ii)
-0.50
,
0.50
(iii)
-2.00
,
2.00
(iv)
0.00
,
0.00
(v)
-1.50
,
1.50
Question
12
12.
Which of the following are true for m > 0 and a > 0?
a)
The curve of a parabola
y
=
−
m
x
2
lies in the I & II quadrant
b)
The curve of a parabola
x
=
−
m
y
2
lies in the I & II quadrant
c)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
lies in the I & II quadrant
d)
The curve of a parabola
x
=
−
m
y
2
lies in the II & III quadrant
e)
The curve of a parabola
y
=
m
x
2
lies in the I & II quadrant
(i)
{b,e,d}
(ii)
{a,d}
(iii)
{c,a,d}
(iv)
{b,e}
(v)
{d,e}
Question
13
13.
The value of the polynomial
(
−
d
e
+
3
f
)
at
d
=
4
,
e
=
2
,
f
=
(-1)
is
(i)
-12
(ii)
-11
(iii)
-9
(iv)
-10
(v)
-13
Question
14
14.
Which of the following equations represents the given graph ?
(i)
y
=
5
x
2
(ii)
y
=
2
x
2
(iii)
y
=
3
x
2
(iv)
y
=
4
x
2
(v)
y
=
7
x
2
Question
15
15.
The remainder when
(
−
7
f
3
−
f
2
+
8
)
is divided by
(
f
2
−
11
f
+
24
)
is
(i)
(
−
691
f
+
1880
)
(ii)
(
−
689
f
+
1880
)
(iii)
(
−
687
f
+
1880
)
(iv)
(
−
693
f
+
1880
)
(v)
(
−
690
f
+
1880
)
Question
16
16.
The coefficient of term
p
in polynomial
(
−
4
p
2
−
4
p
−
7
)
is
(i)
-7
(ii)
-5
(iii)
-2
(iv)
-3
(v)
-4
Question
17
17.
(
12
x
4
+
15
x
3
−
69
x
2
−
18
x
)
÷
(
3
x
2
+
3
x
−
18
)
(i)
(
4
x
2
−
x
)
(ii)
(
4
x
2
+
2
x
)
(iii)
4
x
2
(iv)
(
4
x
2
+
x
)
(v)
(
−
4
x
2
+
x
)
Question
18
18.
If
α
=
9
8
,
β
=
5
6
,
γ
=
8
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
521
168
(ii)
(
−
521
168
)
(iii)
15
14
(iv)
1067
336
(v)
(
−
1067
336
)
Question
19
19.
Find the quadratic equation, the sum of whose roots is
-5
and product is
-6
(i)
(
5
x
−
6
)
=
0
(ii)
(
2
x
2
+
5
x
−
6
)
=
0
(iii)
(
x
2
+
3
x
−
6
)
=
0
(iv)
(
x
2
+
5
x
−
6
)
=
0
(v)
(
x
2
+
8
x
−
6
)
=
0
Question
20
20.
If
α, β, γ
are the roots of the cubic equation
(
504
x
3
−
1097
x
2
+
766
x
−
168
)
=
0
,
find
α + β + γ
(i)
(
−
1
3
)
(ii)
383
252
(iii)
1097
504
(iv)
(
−
383
252
)
(v)
(
−
1097
504
)
Question
21
21.
From the following graph of
y = p(x)
, find the roots of
p(x)
(i)
-7, -5, -1 and -3
(ii)
-7, -5, -4 and -3
(iii)
-7, 6, -4 and -3
(iv)
-8, -5, -4 and -3
(v)
-7, -5, -4 and 3
Question
22
22.
(
6
x
4
+
6
x
3
)
÷
3
x
2
(i)
(
x
2
+
2
x
)
(ii)
(
2
x
2
−
2
x
)
(iii)
(
2
x
2
+
3
x
)
(iv)
(
2
x
2
+
2
x
)
(v)
(
−
2
x
2
+
2
x
)
Question
23
23.
The product of the roots of the quadratic equation
(
x
2
−
10
x
+
25
)
=
0
is
(i)
25
(ii)
24
(iii)
22
(iv)
27
(v)
26
Question
24
24.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
-36
-16
-4
0
-4
-16
-36
(i)
y
=
(
−
7
x
2
)
(ii)
y
=
(
−
4
x
2
)
(iii)
y
=
(
−
5
x
2
)
(iv)
y
=
(
−
2
x
2
)
(v)
y
=
(
−
3
x
2
)
Question
25
25.
Find the quadratic equation, the sum of whose roots is
1
2
and product is
1
16
(i)
(
17
x
2
−
8
x
+
1
)
=
0
(ii)
(
16
x
2
−
11
x
+
1
)
=
0
(iii)
(
15
x
2
−
8
x
+
1
)
=
0
(iv)
(
16
x
2
−
8
x
+
1
)
=
0
(v)
(
16
x
2
−
6
x
+
1
)
=
0
Assignment Key
1) (iv)
2) (iii)
3) (iii)
4) (iv)
5) (ii)
6) (iv)
7) (ii)
8) (i)
9) (i)
10) (ii)
11) (i)
12) (v)
13) (ii)
14) (iv)
15) (v)
16) (v)
17) (iv)
18) (iv)
19) (iv)
20) (iii)
21) (ii)
22) (iv)
23) (i)
24) (ii)
25) (iv)
