EduSahara™ Assignment
Name : Quadratic Equations Miscellaneous
Chapter : Quadratic Equations
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
5
x
+
1
)
(
4
x
+
2
)
=
(
7
x
+
4
)
(
6
x
+
3
)
(i)
(
5
,
(
-1
2
)
)
(ii)
(
-5
,
1
2
)
(iii)
(
8
,
1
2
)
(iv)
(
4
,
-1
)
(v)
(
2
,
(
-3
2
)
)
Question
2
2.
Solve :
(
x
−
11
)
(
x
−
10
)
+
(
x
−
8
)
(
x
−
6
)
=
29
21
(i)
(
15
,
8
)
(ii)
(
14
,
116
15
)
(iii)
(
13
,
102
13
)
(iv)
(
10
,
100
13
)
(v)
(
12
,
8
)
Question
3
3.
Solve :
(
x
2
−
7
x
)
2
−
14
(
x
2
−
7
x
)
+
45
=
0
(i)
(
7
2
+
1
2
√
85
)
,
(
7
2
−
1
2
√
85
)
,
(
7
2
+
1
2
√
69
)
,
(
7
2
−
1
2
√
69
)
(ii)
(
9
2
+
1
2
√
85
)
,
(
9
2
−
1
2
√
85
)
,
(
9
2
+
1
2
√
69
)
,
(
9
2
−
1
2
√
69
)
(iii)
(
5
2
+
1
2
√
85
)
,
(
5
2
−
1
2
√
85
)
,
(
5
2
+
1
2
√
69
)
,
(
5
2
−
1
2
√
69
)
(iv)
(
7
2
+
1
2
4
√
85
)
,
(
7
2
−
1
2
4
√
85
)
,
(
7
2
+
1
2
4
√
69
)
,
(
7
2
−
1
2
4
√
69
)
(v)
(
7
2
+
85
2
)
,
(
7
2
−
85
2
)
,
(
7
2
+
69
2
)
,
(
7
2
−
69
2
)
Question
4
4.
Solve :
(
x
4
−
14
x
2
+
45
)
=
0
(i)
3
,
(
−
3
)
,
√
5
,
(
−
√
5
)
(ii)
0
,
(
−
6
)
,
√
3
,
(
−
√
2
)
(iii)
2
,
(
−
4
)
,
5
,
(
−
5
)
(iv)
5
,
(
−
1
)
,
√
7
,
(
−
√
8
)
(v)
4
,
(
−
2
)
,
4
√
5
,
(
−
4
√
5
)
Question
5
5.
Solve :
(
x
−
1
)
x
(
x
+
1
)
(
x
+
2
)
=
3024
(i)
8
,
(
−
7
)
(ii)
6
,
(
−
9
)
(iii)
4
,
(
−
10
)
(iv)
7
,
(
−
8
)
(v)
10
,
(
−
5
)
Question
6
6.
For what values of
k
are the roots of
(
k
−
3
)
x
2
+
(
k
+
77
)
x
+
(
k
+
14
)
=
0
equal
(i)
(
(
−
151
5
)
,
67
)
(ii)
(
(
−
89
3
)
,
64
)
(iii)
(
(
−
89
3
)
,
66
)
(iv)
(
(
−
151
5
)
,
66
)
(v)
(
(
−
91
3
)
,
67
)
Question
7
7.
If
p
and
q
are the roots of
(
x
2
−
8
x
+
12
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
12
x
2
−
104
x
+
169
)
=
0
(ii)
(
8
x
2
−
70
x
+
117
)
=
0
(iii)
(
12
x
2
−
116
x
+
195
)
=
0
(iv)
(
24
x
2
−
202
x
+
325
)
=
0
(v)
(
12
x
2
−
100
x
+
143
)
=
0
Question
8
8.
If
-4
is the root of
(
x
2
+
k
x
+
20
)
=
0
, find
k
and the other root
(i)
k
=
9
, and the other root =
-5
(ii)
k
=
12
, and the other root =
-3
(iii)
k
=
7
, and the other root =
-8
(iv)
k
=
10
, and the other root =
-4
(v)
k
=
8
, and the other root =
-6
Question
9
9.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
+
1
)
,
(
x
−
6
)
and leaves a remainder of
30
when divided by
(
x
−
9
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
-4
,
c
=
-5
(ii)
a
=
1
,
b
=
-6
,
c
=
-7
(iii)
a
=
1
,
b
=
-7
,
c
=
-9
(iv)
a
=
1
,
b
=
-5
,
c
=
-6
(v)
a
=
1
,
b
=
-3
,
c
=
-4
Question
10
10.
Find
a
and
b
in order that
(
x
3
+
4
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
−
3
x
−
54
)
(i)
a
=
-76
,
b
=
-379
(ii)
a
=
-75
,
b
=
-378
(iii)
a
=
-77
,
b
=
-381
(iv)
a
=
-73
,
b
=
-376
(v)
a
=
-74
,
b
=
-377
Question
11
11.
Find the quadratic equation with roots
(
(
-3
2
)
,
(
-3
2
)
)
(i)
(
4
x
2
+
8
x
+
3
)
=
0
(ii)
(
4
x
2
+
16
x
+
15
)
=
0
(iii)
(
8
x
2
+
18
x
+
9
)
=
0
(iv)
(
2
x
2
+
9
x
+
9
)
=
0
(v)
(
4
x
2
+
12
x
+
9
)
=
0
Assignment Key
1) (i)
2) (iii)
3) (i)
4) (i)
5) (iv)
6) (v)
7) (i)
8) (i)
9) (iv)
10) (ii)
11) (v)
