EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The sum of the roots of the quadratic equation
(
x
2
−
4
x
+
4
)
=
0
is
(i)
1
(ii)
4
(iii)
6
(iv)
5
(v)
3
Question
2
2.
The product of the roots of the quadratic equation
(
−
54
x
2
−
90
x
−
36
)
=
0
is
(i)
4
3
(ii)
2
(iii)
2
5
(iv)
2
3
(v)
0
Question
3
3.
Solve :
(
3
x
+
2
)
(
x
+
2
)
+
(
x
−
1
)
(
4
x
+
1
)
=
153
65
(i)
(
4
,
(
-102
235
)
)
(ii)
(
3
,
(
-102
233
)
)
(iii)
(
1
,
(
-104
233
)
)
(iv)
(
2
,
(
-34
77
)
)
(v)
(
5
,
(
-100
233
)
)
Question
4
4.
The product of the roots of the quadratic equation
(
x
2
−
4
x
+
4
)
=
0
is
(i)
3
(ii)
5
(iii)
6
(iv)
1
(v)
4
Question
5
5.
Solve :
√
(
2
x
2
+
7
x
−
9
)
=
(
x
−
5
)
(i)
(
−
17
2
−
5
2
√
17
)
,
(
−
17
2
+
5
2
√
17
)
(ii)
(
−
17
2
√
5
−
5
2
√
17
)
,
(
−
17
2
√
5
+
5
2
√
17
)
(iii)
(
−
17
2
−
5
2
√
51
)
,
(
−
17
2
+
5
2
√
51
)
(iv)
(
−
17
2
−
5
2
√
34
)
,
(
−
17
2
+
5
2
√
34
)
(v)
(
−
17
2
√
4
−
5
2
√
17
)
,
(
−
17
2
√
4
+
5
2
√
17
)
Question
6
6.
The sum of the roots of the quadratic equation
(
3
x
2
−
21
x
+
36
)
=
0
is
(i)
9
(ii)
8
(iii)
6
(iv)
4
(v)
7
Question
7
7.
Find the roots of the quadratic equation
(
x
2
+
14
x
+
48
)
=
0
(i)
(
-6
,
-8
)
(ii)
(
-5
,
-8
)
(iii)
(
-5
,
-9
)
(iv)
(
-3
,
-9
)
(v)
(
-3
,
-10
)
Question
8
8.
Solve :
9
x
2
b
2
−
a
2
= 0
(i)
a
b
,
a
3
b
(ii)
a
b
,
−
a
b
(iii)
−
a
3
b
,
−
a
b
(iv)
a
5
b
,
−
a
5
b
(v)
a
3
b
,
−
a
3
b
Question
9
9.
Solve :
56
x
2
+
7
x
+
16
x
b
+
2
b
= 0
(i)
−
1
8
,
−
2
b
7
(ii)
−
3
8
,
−
4
b
7
(iii)
−
1
10
,
−
2
b
9
(iv)
−
1
6
,
−
2
b
5
(v)
1
8
,
0
Question
10
10.
Solve :
15
x
2
b
2
−
2
x
b
−
1
= 0
(i)
1
2
b
,
−
1
3
b
(ii)
1
4
b
,
−
1
7
b
(iii)
0
,
−
3
5
b
(iv)
2
3
b
,
1
5
b
(v)
2
6
b
,
−
1
5
b
Question
11
11.
For what values of
k
are the roots of
(
k
−
24
)
x
2
+
k
x
+
(
k
+
21
)
=
0
equal
(i)
(
(
−
22
)
,
27
)
(ii)
(
(
−
24
)
,
28
)
(iii)
(
(
−
22
)
,
25
)
(iv)
(
(
−
23
)
,
27
)
(v)
(
(
−
23
)
,
28
)
Question
12
12.
Solve :
64
x
2
−
16
√
2
x
+
2
=
0
(i)
√
2
8
√
4
,
√
2
8
√
4
(ii)
√
2
8
,
√
2
8
(iii)
√
8
8
,
√
8
8
(iv)
√
2
8
,
√
2
8
√
4
(v)
√
8
8
,
√
2
8
Question
13
13.
Solve :
30
x
2
−
31
a
b
x
+
5
a
2
b
2
= 0
(i)
5
a
b
6
,
a
b
5
(ii)
5
a
b
8
,
a
b
7
(iii)
5
a
b
4
,
a
b
3
(iv)
7
a
b
6
,
3
a
b
5
(v)
a
b
2
,
−
a
b
5
Question
14
14.
Solve :
6
x
2
b
4
−
5
a
x
b
2
+
a
2
= 0
(i)
a
b
2
,
a
b
2
(ii)
a
2
b
2
,
a
3
b
2
(iii)
−
a
2
b
2
,
−
a
3
b
2
(iv)
a
4
b
2
,
a
5
b
2
(v)
3
a
2
b
2
,
a
b
2
Question
15
15.
Find the quadratic equation, the sum of whose roots is
4
3
and product is
4
9
(i)
(
9
x
2
−
9
x
+
4
)
=
0
(ii)
(
9
x
2
−
14
x
+
4
)
=
0
(iii)
(
10
x
2
−
12
x
+
4
)
=
0
(iv)
(
8
x
2
−
12
x
+
4
)
=
0
(v)
(
9
x
2
−
12
x
+
4
)
=
0
Question
16
16.
Solve :
−
5
(
−
x
−
4
)
−
1
(
x
+
5
)
=
3
(
x
+
2
)
(i)
(
−
1
−
√
19
)
,
(
−
1
+
√
19
)
(ii)
(
−
1
−
√
57
)
,
(
−
1
+
√
57
)
(iii)
(
−
√
4
−
√
19
)
,
(
−
√
4
+
√
19
)
(iv)
(
−
√
5
−
√
19
)
,
(
−
√
5
+
√
19
)
(v)
(
−
1
−
√
38
)
,
(
−
1
+
√
38
)
Question
17
17.
Solve :
63
x
2
+
17
a
x
−
20
a
2
= 0
(i)
−
5
a
9
,
4
a
11
(ii)
−
3
a
7
,
2
a
3
(iii)
−
5
a
7
,
4
a
9
(iv)
−
a
,
4
a
7
(v)
−
a
,
2
a
9
Question
18
18.
The product of the roots of the quadratic equation
(
25
x
2
−
90
x
+
81
)
=
0
is
(i)
79
25
(ii)
81
25
(iii)
83
25
(iv)
75
23
(v)
29
9
Question
19
19.
If
p
and
q
are the roots of
(
x
2
−
9
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
3
x
2
+
2
x
−
16
)
=
0
(ii)
(
3
x
2
−
2
x
−
16
)
=
0
(iii)
(
9
x
2
−
64
)
=
0
(iv)
(
3
x
2
−
4
x
−
32
)
=
0
(v)
(
15
x
2
−
4
x
−
96
)
=
0
Question
20
20.
Solve the quadratic equation
x
−
7
=
8
x
(i)
(
9
,
-2
)
(ii)
(
8
,
-1
)
(iii)
(
10
,
-3
)
(iv)
(
10
,
-2
)
(v)
(
9
,
-1
)
Question
21
21.
Solve :
(
7
x
+
1
)
(
19
x
+
1
)
=
(
17
x
+
1
)
(
45
x
+
1
)
(i)
(
3
,
4
)
(ii)
(
0
,
2
)
(iii)
(
0
,
-2
)
(iv)
(
-2
,
-1
)
(v)
(
-1
,
1
)
Question
22
22.
Solve :
−
7
√
11
x
2
+
52
x
+
9
√
11
=
0
(i)
√
11
(
−
7
√
4
)
,
9
√
44
(ii)
√
44
(
−
7
)
,
9
√
11
(iii)
√
11
(
−
7
)
,
9
√
11
(iv)
√
44
(
−
7
)
,
9
√
4
√
11
(v)
√
11
(
−
7
)
,
9
√
44
Question
23
23.
If
-5
is the root of
(
x
2
+
k
x
+
20
)
=
0
, find
k
and the other root
(i)
k
=
6
, and the other root =
-7
(ii)
k
=
9
, and the other root =
-4
(iii)
k
=
8
, and the other root =
-5
(iv)
k
=
11
, and the other root =
-2
(v)
k
=
10
, and the other root =
-3
Question
24
24.
Solve :
(
x
+
7
)
(
x
+
8
)
(
x
+
9
)
(
x
+
10
)
=
360
(i)
(
−
3
)
,
(
−
12
)
(ii)
(
−
4
)
,
(
−
13
)
(iii)
(
−
2
)
,
(
−
11
)
(iv)
(
−
6
)
,
(
−
16
)
(v)
(
−
5
)
,
(
−
14
)
Question
25
25.
Find the quadratic equation, the sum of whose roots is
-16
and product is
64
(i)
(
16
x
+
64
)
=
0
(ii)
(
2
x
2
+
16
x
+
64
)
=
0
(iii)
(
x
2
+
13
x
+
64
)
=
0
(iv)
(
x
2
+
16
x
+
64
)
=
0
(v)
(
x
2
+
18
x
+
64
)
=
0
Assignment Key
1) (ii)
2) (iv)
3) (ii)
4) (v)
5) (i)
6) (v)
7) (i)
8) (v)
9) (i)
10) (v)
11) (ii)
12) (ii)
13) (i)
14) (ii)
15) (v)
16) (i)
17) (iii)
18) (ii)
19) (iii)
20) (ii)
21) (ii)
22) (iii)
23) (ii)
24) (ii)
25) (iv)
