EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
30
x
2
+
19
a
b
x
−
4
a
2
b
2
= 0
(i)
−
2
a
b
5
,
a
b
2
(ii)
−
4
a
b
5
,
a
b
6
(iii)
−
4
a
b
3
,
a
b
4
(iv)
−
4
a
b
7
,
a
b
8
(v)
−
6
a
b
5
,
−
a
b
6
Question
2
2.
Find the discriminant of the quadratic equation
(
−
5
x
2
+
12
x
+
9
)
=
0
(i)
322
(ii)
323
(iii)
325
(iv)
324
(v)
326
Question
3
3.
Solve :
12
x
2
+
2
√
3
x
−
72
=
0
(i)
8
√
4
√
12
,
(
−
9
√
4
)
√
12
(ii)
8
√
12
,
(
−
9
)
√
48
(iii)
8
√
4
√
12
,
(
−
9
)
√
12
(iv)
8
√
12
,
(
−
9
)
√
12
(v)
8
√
48
,
(
−
9
)
√
48
Question
4
4.
Solve :
12
x
2
−
17
a
2
b
x
+
6
a
4
b
2
= 0
(i)
4
a
2
b
3
,
5
a
2
b
4
(ii)
0
,
a
2
b
4
(iii)
2
a
2
b
,
3
a
2
b
2
(iv)
2
a
2
b
5
,
a
2
b
2
(v)
2
a
2
b
3
,
3
a
2
b
4
Question
5
5.
Solve :
16
x
2
a
−
8
x
−
10
x
a
+
5
= 0
(i)
1
a
,
5
6
(ii)
1
a
,
7
8
(iii)
0
,
3
8
(iv)
2
4
a
,
5
8
(v)
1
3
a
,
1
2
Question
6
6.
Solve :
(
3
x
+
1
)
(
7
x
+
1
)
=
(
11
x
+
2
)
(
25
x
+
2
)
(i)
(
-3
,
0
)
(ii)
(
0
,
3
)
(iii)
(
2
,
6
)
(iv)
(
0
,
-3
)
(v)
(
-1
,
2
)
Question
7
7.
Find the quadratic equation, the sum of whose roots is
(
-8
3
)
and product is
16
9
(i)
(
35
x
2
+
96
x
+
64
)
=
0
(ii)
(
37
x
2
+
96
x
+
64
)
=
0
(iii)
(
36
x
2
+
99
x
+
64
)
=
0
(iv)
(
36
x
2
+
93
x
+
64
)
=
0
(v)
(
36
x
2
+
96
x
+
64
)
=
0
Question
8
8.
Find the discriminant of the quadratic equation
(
−
4
x
2
+
11
x
−
6
)
=
0
(i)
24
(ii)
23
(iii)
28
(iv)
25
(v)
26
Question
9
9.
Solve :
6
x
2
b
2
+
a
2
x
b
−
a
4
= 0
(i)
−
a
2
b
,
a
2
b
(ii)
a
2
2
b
,
a
2
b
(iii)
−
a
2
4
b
,
a
2
5
b
(iv)
−
3
a
2
2
b
,
−
a
2
3
b
(v)
−
a
2
2
b
,
a
2
3
b
Question
10
10.
If
p
and
q
are the roots of
(
x
2
+
x
−
42
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
42
x
2
+
41
x
−
1681
)
=
0
(ii)
(
42
x
2
+
55
x
−
1763
)
=
0
(iii)
(
42
x
2
+
29
x
−
1763
)
=
0
(iv)
(
18
x
2
+
21
x
−
697
)
=
0
(v)
(
28
x
2
+
39
x
−
1189
)
=
0
Question
11
11.
Find the quadratic equation with roots
(
(
-1
5
)
,
(
-7
8
)
)
(i)
(
50
x
2
+
45
x
+
7
)
=
0
(ii)
(
40
x
2
+
59
x
+
21
)
=
0
(iii)
(
40
x
2
+
43
x
+
7
)
=
0
(iv)
(
24
x
2
+
29
x
+
7
)
=
0
(v)
(
40
x
2
+
33
x
+
5
)
=
0
Question
12
12.
Solve :
(
x
2
−
7
x
)
2
−
9
(
x
2
−
7
x
)
+
18
=
0
(i)
(
7
2
+
1
2
4
√
73
)
,
(
7
2
−
1
2
4
√
73
)
,
(
7
2
+
1
2
4
√
61
)
,
(
7
2
−
1
2
4
√
61
)
(ii)
(
7
2
+
73
2
)
,
(
7
2
−
73
2
)
,
(
7
2
+
61
2
)
,
(
7
2
−
61
2
)
(iii)
(
5
2
+
1
2
√
73
)
,
(
5
2
−
1
2
√
73
)
,
(
5
2
+
1
2
√
61
)
,
(
5
2
−
1
2
√
61
)
(iv)
(
7
2
+
1
2
√
73
)
,
(
7
2
−
1
2
√
73
)
,
(
7
2
+
1
2
√
61
)
,
(
7
2
−
1
2
√
61
)
(v)
(
9
2
+
1
2
√
73
)
,
(
9
2
−
1
2
√
73
)
,
(
9
2
+
1
2
√
61
)
,
(
9
2
−
1
2
√
61
)
Question
13
13.
Solve :
14
x
2
b
4
+
5
a
x
b
2
−
a
2
= 0
(i)
a
2
b
2
,
3
a
7
b
2
(ii)
−
a
4
b
2
,
a
9
b
2
(iii)
−
a
b
2
,
a
5
b
2
(iv)
−
3
a
2
b
2
,
−
a
7
b
2
(v)
−
a
2
b
2
,
a
7
b
2
Question
14
14.
The sum of the roots of the quadratic equation
(
64
x
2
−
128
x
+
64
)
=
0
is
(i)
0
(ii)
2
(iii)
1
(iv)
4
(v)
3
Question
15
15.
Solve :
10
x
2
−
a
b
2
x
−
3
a
2
b
4
= 0
(i)
a
b
2
5
,
−
3
a
b
2
2
(ii)
a
b
2
,
−
a
b
2
(iii)
3
a
b
2
5
,
−
a
b
2
2
(iv)
a
b
2
,
a
b
2
2
(v)
3
a
b
2
7
,
−
a
b
2
4
Question
16
16.
Solve :
10
x
2
b
−
5
x
b
−
6
x
+
3
= 0
(i)
1
6
,
1
5
b
(ii)
3
4
,
1
b
(iii)
5
6
,
1
b
(iv)
3
8
,
3
7
b
(v)
3
6
,
3
5
b
Question
17
17.
Solve :
14
x
2
a
2
+
11
b
2
x
a
+
2
b
4
= 0
(i)
−
b
2
4
a
,
−
2
b
2
9
a
(ii)
−
3
b
2
2
a
,
−
4
b
2
7
a
(iii)
−
b
2
a
,
−
2
b
2
5
a
(iv)
b
2
2
a
,
0
(v)
−
b
2
2
a
,
−
2
b
2
7
a
Question
18
18.
Find the quadratic equation, the sum of whose roots is
-18
and product is
81
(i)
(
x
2
+
16
x
+
81
)
=
0
(ii)
(
18
x
+
81
)
=
0
(iii)
(
2
x
2
+
18
x
+
81
)
=
0
(iv)
(
x
2
+
21
x
+
81
)
=
0
(v)
(
x
2
+
18
x
+
81
)
=
0
Question
19
19.
Solve :
(
x
4
−
11
x
2
+
30
)
=
0
(i)
√
6
,
(
−
√
6
)
,
√
5
,
(
−
√
5
)
(ii)
√
9
,
(
−
√
8
)
,
√
8
,
(
−
√
7
)
(iii)
4
√
6
,
(
−
4
√
6
)
,
4
√
5
,
(
−
4
√
5
)
(iv)
√
4
,
(
−
√
4
)
,
√
3
,
(
−
√
3
)
(v)
6
,
(
−
6
)
,
5
,
(
−
5
)
Question
20
20.
Solve the quadratic equation
x
−
7
x
=
6
(i)
(
8
,
-2
)
(ii)
(
9
,
-2
)
(iii)
(
8
,
-1
)
(iv)
(
7
,
-1
)
(v)
(
9
,
-4
)
Question
21
21.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
−
7
)
,
(
x
+
5
)
and leaves a remainder of
-32
when divided by
(
x
−
3
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
-5
,
c
=
-37
(ii)
a
=
1
,
b
=
-2
,
c
=
-35
(iii)
a
=
1
,
b
=
-3
,
c
=
-36
(iv)
a
=
1
,
b
=
1
,
c
=
-33
(v)
a
=
1
,
b
=
-1
,
c
=
-34
Question
22
22.
The product of the roots of the quadratic equation
(
x
2
+
2
x
+
1
)
=
0
is
(i)
3
(ii)
1
(iii)
2
(iv)
0
(v)
-2
Question
23
23.
Find
a
and
b
in order that
(
x
3
+
16
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
+
7
x
−
8
)
(i)
a
=
56
,
b
=
-71
(ii)
a
=
57
,
b
=
-69
(iii)
a
=
54
,
b
=
-73
(iv)
a
=
53
,
b
=
-74
(v)
a
=
55
,
b
=
-72
Question
24
24.
Solve :
18
x
2
a
4
b
2
−
9
x
a
2
b
+
1
= 0
(i)
1
4
a
2
b
,
3
7
a
2
b
(ii)
1
2
a
2
b
,
5
9
a
2
b
(iii)
1
8
a
2
b
,
3
11
a
2
b
(iv)
1
6
a
2
b
,
3
9
a
2
b
(v)
−
1
6
a
2
b
,
1
9
a
2
b
Question
25
25.
Find the roots of the quadratic equation
(
−
3
x
2
−
3
x
+
7
)
=
0
(i)
(
(
−
1
2
−
1
6
√
93
)
,
(
−
1
2
+
1
6
√
93
)
)
(ii)
(
(
−
1
2
−
1
6
4
√
93
)
,
(
−
1
2
+
31
2
)
)
(iii)
(
(
1
2
−
1
6
√
93
)
,
(
−
1
2
+
31
2
)
)
(iv)
(
(
1
2
−
1
6
√
93
)
,
(
−
3
2
+
1
6
√
93
)
)
(v)
(
(
−
1
2
−
1
6
4
√
93
)
,
(
−
1
2
+
1
6
√
93
)
)
Assignment Key
1) (ii)
2) (iv)
3) (iv)
4) (v)
5) (iv)
6) (ii)
7) (v)
8) (iv)
9) (v)
10) (i)
11) (iii)
12) (iv)
13) (v)
14) (ii)
15) (iii)
16) (v)
17) (v)
18) (v)
19) (i)
20) (iv)
21) (ii)
22) (ii)
23) (v)
24) (iv)
25) (i)
