EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
56
x
2
a
2
+
27
b
2
x
a
−
18
b
4
= 0
(i)
−
6
b
2
7
a
,
3
b
2
8
a
(ii)
−
2
b
2
3
a
,
3
b
2
10
a
(iii)
−
4
b
2
7
a
,
5
b
2
8
a
(iv)
−
8
b
2
7
a
,
b
2
8
a
(v)
−
6
b
2
5
a
,
b
2
2
a
Question
2
2.
Solve the quadratic equation
x
+
1
=
2
x
(i)
(
4
,
-5
)
(ii)
(
4
,
-3
)
(iii)
(
1
,
-2
)
(iv)
(
2
,
-2
)
(v)
(
2
,
-3
)
Question
3
3.
Solve :
28
x
2
−
20
x
−
7
x
b
+
5
b
= 0
(i)
5
7
,
b
4
(ii)
1
,
b
2
(iii)
1
,
3
b
4
(iv)
5
9
,
b
6
(v)
3
7
,
−
b
4
Question
4
4.
Solve :
√
(
4
x
+
7
)
=
(
x
−
7
)
(i)
(
9
+
√
39
)
,
(
9
−
√
39
)
(ii)
(
9
+
√
117
)
,
(
9
−
√
117
)
(iii)
(
9
√
4
+
√
39
)
,
(
9
√
4
−
√
39
)
(iv)
(
9
+
√
78
)
,
(
9
−
√
78
)
(v)
(
9
√
5
+
√
39
)
,
(
9
√
5
−
√
39
)
Question
5
5.
Find the quadratic equation with roots
(
-2
,
-2
)
(i)
(
x
2
+
3
x
+
2
)
=
0
(ii)
(
x
2
+
7
x
+
10
)
=
0
(iii)
(
x
2
+
5
x
+
6
)
=
0
(iv)
(
x
2
+
4
x
+
4
)
=
0
(v)
(
x
2
+
2
x
)
=
0
Question
6
6.
Solve :
36
x
2
+
13
a
2
b
x
+
a
4
b
2
= 0
(i)
a
2
b
9
,
a
2
b
4
(ii)
−
a
2
b
9
,
−
a
2
b
4
(iii)
−
a
2
b
11
,
−
a
2
b
6
(iv)
−
a
2
b
3
,
−
3
a
2
b
4
(v)
−
a
2
b
7
,
−
a
2
b
2
Question
7
7.
Solve :
12
x
2
+
10
√
3
x
−
14
=
0
(i)
2
√
12
,
(
−
7
)
√
12
(ii)
2
√
4
√
12
,
(
−
7
)
√
12
(iii)
2
√
4
√
12
,
(
−
7
√
4
)
√
12
(iv)
2
√
12
,
(
−
7
)
√
48
(v)
2
√
48
,
(
−
7
)
√
48
Question
8
8.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
+
6
)
,
(
x
−
2
)
and leaves a remainder of
20
when divided by
(
x
+
8
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
7
,
c
=
-10
(ii)
a
=
1
,
b
=
5
,
c
=
-11
(iii)
a
=
1
,
b
=
4
,
c
=
-12
(iv)
a
=
1
,
b
=
2
,
c
=
-15
(v)
a
=
1
,
b
=
3
,
c
=
-13
Question
9
9.
Solve :
8
x
2
a
−
6
x
−
4
x
a
+
3
= 0
(i)
6
8
a
,
2
4
(ii)
1
2
a
,
0
(iii)
3
5
a
,
1
3
(iv)
1
a
,
1
Question
10
10.
Solve :
6
x
2
+
a
b
x
−
a
2
b
2
= 0
(i)
−
a
b
6
,
a
b
(ii)
−
3
a
b
4
,
a
b
(iii)
−
3
a
b
8
,
a
b
5
(iv)
−
5
a
b
6
,
−
a
b
3
(v)
−
a
b
2
,
a
b
3
Question
11
11.
For what values of
k
are the roots of
(
k
−
34
)
x
2
+
(
k
+
1
)
x
+
(
k
−
23
)
=
0
equal
(i)
(
87
5
,
59
)
(ii)
(
87
5
,
58
)
(iii)
(
55
3
,
58
)
(iv)
(
53
3
,
59
)
(v)
(
55
3
,
56
)
Question
12
12.
Find the quadratic equation with roots
(
1
4
,
1
4
)
(i)
(
24
x
2
−
10
x
+
1
)
=
0
(ii)
(
16
x
2
−
16
x
+
3
)
=
0
(iii)
(
8
x
2
−
6
x
+
1
)
=
0
(iv)
(
16
x
2
−
8
x
+
1
)
=
0
(v)
(
16
x
2
−
1
)
=
0
Question
13
13.
Find the quadratic equation with roots
(
3
,
1
)
(i)
(
x
2
−
5
x
+
6
)
=
0
(ii)
(
x
2
−
3
x
+
2
)
=
0
(iii)
(
x
2
−
6
x
+
9
)
=
0
(iv)
(
x
2
−
2
x
+
1
)
=
0
(v)
(
x
2
−
4
x
+
3
)
=
0
Question
14
14.
Find the roots of the quadratic equation
(
−
4
x
2
−
8
x
−
2
)
=
0
(i)
(
(
1
−
1
2
√
2
)
,
(
−
1
+
1
)
)
(ii)
(
(
1
−
1
2
√
2
)
,
(
−
4
+
1
2
√
2
)
)
(iii)
(
(
−
1
−
1
2
4
√
2
)
,
(
−
1
+
1
)
)
(iv)
(
(
−
1
−
1
2
4
√
2
)
,
(
−
1
+
1
2
√
2
)
)
(v)
(
(
−
1
−
1
2
√
2
)
,
(
−
1
+
1
2
√
2
)
)
Question
15
15.
Solve :
x
2
−
18
x
+
76
=
0
(i)
(
9
√
4
+
√
5
)
,
(
9
√
4
−
√
5
)
(ii)
(
9
+
√
15
)
,
(
9
−
√
15
)
(iii)
(
9
√
5
+
√
5
)
,
(
9
√
5
−
√
5
)
(iv)
(
9
+
√
5
)
,
(
9
−
√
5
)
(v)
(
9
+
√
10
)
,
(
9
−
√
10
)
Question
16
16.
Find
a
and
b
in order that
(
x
3
−
9
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
−
25
)
(i)
a
=
-23
,
b
=
227
(ii)
a
=
-25
,
b
=
225
(iii)
a
=
-24
,
b
=
226
(iv)
a
=
-26
,
b
=
224
(v)
a
=
-27
,
b
=
223
Question
17
17.
Solve :
16
x
2
b
4
−
22
a
x
b
2
+
7
a
2
= 0
(i)
a
b
2
,
9
a
8
b
2
(ii)
2
a
4
b
2
,
7
a
8
b
2
(iii)
a
3
b
2
,
7
a
10
b
2
(iv)
a
b
2
,
7
a
6
b
2
(v)
0
,
5
a
8
b
2
Question
18
18.
Solve :
(
30
x
+
1
)
(
11
x
+
2
)
=
(
47
x
+
2
)
(
18
x
+
1
)
(i)
(
-3
,
1
23
)
(ii)
(
6
,
1
23
)
(iii)
(
0
,
(
-3
23
)
)
(iv)
(
2
,
(
-1
21
)
)
(v)
(
3
,
(
-1
23
)
)
Question
19
19.
Solve :
36
x
2
−
43
a
b
2
x
+
12
a
2
b
4
= 0
(i)
3
a
b
2
5
,
4
a
b
2
11
(ii)
a
b
2
,
2
a
b
2
3
(iii)
a
b
2
2
,
2
a
b
2
9
(iv)
6
a
b
2
8
,
4
a
b
2
9
(v)
a
b
2
,
4
a
b
2
7
Question
20
20.
Solve :
3
(
−
x
−
5
)
−
5
(
x
+
4
)
=
−
4
(i)
(
−
5
√
2
)
,
(
−
4
√
2
)
(ii)
(
−
5
√
5
)
,
(
−
4
√
5
)
(iii)
(
−
5
)
,
(
−
4
)
(iv)
(
−
5
√
4
)
,
(
−
4
√
4
)
(v)
(
−
5
√
3
)
,
(
−
4
√
3
)
Question
21
21.
Find the discriminant of the quadratic equation
(
−
4
x
2
+
3
x
+
1
)
=
0
(i)
26
(ii)
22
(iii)
25
(iv)
27
(v)
24
Question
22
22.
Solve :
(
x
−
4
)
(
x
−
5
)
+
(
x
+
6
)
(
x
−
2
)
=
41
10
(i)
(
4
,
5
)
(ii)
(
22
5
,
6
)
(iii)
(
30
7
,
7
)
(iv)
(
32
7
,
9
)
(v)
(
38
9
,
8
)
Question
23
23.
Solve :
21
x
2
a
4
b
2
−
20
x
a
2
b
+
4
= 0
(i)
0
,
0
(ii)
2
9
a
2
b
,
2
5
a
2
b
(iii)
2
7
a
2
b
,
2
3
a
2
b
(iv)
4
7
a
2
b
,
4
3
a
2
b
(v)
2
5
a
2
b
,
2
a
2
b
Question
24
24.
Find the quadratic equation with roots
(
(
-5
2
)
,
(
-3
4
)
)
(i)
(
8
x
2
+
26
x
+
15
)
=
0
(ii)
(
4
x
2
+
23
x
+
15
)
=
0
(iii)
(
8
x
2
+
22
x
+
5
)
=
0
(iv)
(
4
x
2
+
12
x
+
5
)
=
0
(v)
(
8
x
2
+
34
x
+
21
)
=
0
Question
25
25.
Solve :
14
x
2
+
6
a
x
+
7
x
+
3
a
= 0
(i)
−
a
7
,
1
2
(ii)
−
a
3
,
−
1
4
(iii)
−
5
a
7
,
−
3
2
(iv)
−
3
a
5
,
−
1
(v)
−
3
a
7
,
−
1
2
Assignment Key
1) (i)
2) (iii)
3) (i)
4) (i)
5) (iv)
6) (ii)
7) (i)
8) (iii)
9) (i)
10) (v)
11) (iv)
12) (iv)
13) (v)
14) (v)
15) (iv)
16) (ii)
17) (ii)
18) (v)
19) (iv)
20) (iii)
21) (iii)
22) (iii)
23) (iii)
24) (i)
25) (v)
