EduSahara™ Assignment
Name : Quadratic Equations Miscellaneous
Chapter : Quadratic Equations
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
6
x
+
3
)
(
4
x
+
1
)
=
(
28
x
+
3
)
(
18
x
+
1
)
(i)
(
0
,
5
)
(ii)
(
2
,
7
)
(iii)
(
0
,
-5
)
(iv)
(
-3
,
2
)
(v)
(
-1
,
4
)
Question
2
2.
Solve :
(
2
x
+
1
)
(
x
−
1
)
+
(
4
x
+
1
)
(
3
x
+
2
)
=
103
22
(i)
(
(
-76
87
)
,
2
)
(ii)
(
(
-78
89
)
,
0
)
(iii)
(
(
-76
89
)
,
3
)
(iv)
(
(
-74
89
)
,
5
)
(v)
(
(
-76
91
)
,
4
)
Question
3
3.
Solve :
(
x
2
−
4
x
)
2
−
9
(
x
2
−
4
x
)
+
14
=
0
(i)
(
2
+
4
√
11
)
,
(
2
−
4
√
11
)
,
(
2
+
4
√
6
)
,
(
2
−
4
√
6
)
(ii)
(
2
+
√
11
)
,
(
2
−
√
11
)
,
(
2
+
√
6
)
,
(
2
−
√
6
)
(iii)
(
2
+
11
)
,
(
2
−
11
)
,
(
2
+
6
)
,
(
2
−
6
)
(iv)
(
4
+
√
11
)
,
(
4
−
√
11
)
,
(
4
+
√
6
)
,
(
4
−
√
6
)
(v)
(
−
1
+
√
11
)
,
(
0
−
√
11
)
,
(
0
+
√
6
)
,
(
−
1
−
√
6
)
Question
4
4.
Solve :
(
x
4
−
9
x
2
+
14
)
=
0
(i)
7
,
(
−
7
)
,
2
,
(
−
2
)
(ii)
4
√
7
,
(
−
4
√
7
)
,
4
√
2
,
(
−
4
√
2
)
(iii)
√
9
,
(
−
√
9
)
,
√
4
,
(
−
√
4
)
(iv)
√
4
,
(
−
√
5
)
,
√
-1
,
(
−
√
-1
)
(v)
√
7
,
(
−
√
7
)
,
√
2
,
(
−
√
2
)
Question
5
5.
Solve :
(
x
+
5
)
(
x
+
6
)
(
x
+
7
)
(
x
+
8
)
=
3024
(i)
0
,
(
−
15
)
(ii)
2
,
(
−
13
)
(iii)
1
,
(
−
14
)
(iv)
4
,
(
−
11
)
(v)
(
−
2
)
,
(
−
16
)
Question
6
6.
For what values of
k
are the roots of
(
k
−
39
)
x
2
+
(
k
+
21
)
x
+
(
k
−
11
)
=
0
equal
(i)
(
27
5
,
75
)
(ii)
(
27
5
,
74
)
(iii)
(
19
3
,
72
)
(iv)
(
17
3
,
75
)
(v)
(
19
3
,
74
)
Question
7
7.
If
p
and
q
are the roots of
(
x
2
+
9
x
+
14
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
14
x
2
+
149
x
+
255
)
=
0
(ii)
(
14
x
2
+
131
x
+
195
)
=
0
(iii)
(
18
x
2
+
173
x
+
285
)
=
0
(iv)
(
14
x
2
+
135
x
+
225
)
=
0
(v)
(
7
x
2
+
71
x
+
120
)
=
0
Question
8
8.
If
1
is the root of
(
x
2
+
k
x
−
3
)
=
0
, find
k
and the other root
(i)
k
=
-1
, and the other root =
-5
(ii)
k
=
2
, and the other root =
-3
(iii)
k
=
1
, and the other root =
-4
(iv)
k
=
4
, and the other root =
-1
(v)
k
=
3
, and the other root =
-2
Question
9
9.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
+
2
)
,
(
x
+
9
)
and leaves a remainder of
144
when divided by
(
x
−
7
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
11
,
c
=
18
(ii)
a
=
1
,
b
=
8
,
c
=
16
(iii)
a
=
1
,
b
=
10
,
c
=
17
(iv)
a
=
1
,
b
=
14
,
c
=
21
(v)
a
=
1
,
b
=
12
,
c
=
19
Question
10
10.
Find
a
and
b
in order that
(
x
3
−
18
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
−
16
x
+
63
)
(i)
a
=
97
,
b
=
-124
(ii)
a
=
94
,
b
=
-127
(iii)
a
=
96
,
b
=
-125
(iv)
a
=
95
,
b
=
-126
(v)
a
=
93
,
b
=
-128
Question
11
11.
Find the quadratic equation with roots
(
9
7
,
9
7
)
(i)
(
35
x
2
−
108
x
+
81
)
=
0
(ii)
(
49
x
2
−
140
x
+
99
)
=
0
(iii)
(
7
x
2
−
16
x
+
9
)
=
0
(iv)
(
49
x
2
−
126
x
+
81
)
=
0
Assignment Key
1) (i)
2) (iii)
3) (ii)
4) (v)
5) (iii)
6) (iv)
7) (iv)
8) (ii)
9) (i)
10) (iv)
11) (iv)
