EduSahara™ Assignment
Name : Solving some complex Quadratic Equations
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
8
x
+
3
)
(
3
x
+
2
)
=
(
3
x
+
6
)
(
x
+
4
)
(i)
(
-1
,
10
)
(ii)
(
-3
,
8
)
(iii)
(
0
,
11
)
(iv)
(
0
,
-11
)
(v)
(
3
,
13
)
Question
2
2.
Solve :
(
x
−
4
)
(
x
−
8
)
+
(
x
+
2
)
(
x
−
6
)
=
74
15
(i)
(
78
11
,
11
)
(ii)
(
80
11
,
14
)
(iii)
(
64
9
,
10
)
(iv)
(
76
11
,
9
)
(v)
(
92
13
,
12
)
Question
3
3.
Solve :
(
x
2
−
7
x
)
2
−
10
(
x
2
−
7
x
)
+
9
=
0
(i)
(
9
2
+
1
2
√
85
)
,
(
9
2
−
1
2
√
85
)
,
(
9
2
+
1
2
√
53
)
,
(
9
2
−
1
2
√
53
)
(ii)
(
7
2
+
1
2
√
85
)
,
(
7
2
−
1
2
√
85
)
,
(
7
2
+
1
2
√
53
)
,
(
7
2
−
1
2
√
53
)
(iii)
(
5
2
+
1
2
√
85
)
,
(
5
2
−
1
2
√
85
)
,
(
5
2
+
1
2
√
53
)
,
(
5
2
−
1
2
√
53
)
(iv)
(
7
2
+
1
2
4
√
85
)
,
(
7
2
−
1
2
4
√
85
)
,
(
7
2
+
1
2
4
√
53
)
,
(
7
2
−
1
2
4
√
53
)
(v)
(
7
2
+
85
2
)
,
(
7
2
−
85
2
)
,
(
7
2
+
53
2
)
,
(
7
2
−
53
2
)
Question
4
4.
Solve :
(
x
4
−
12
x
2
+
27
)
=
0
(i)
4
,
(
−
2
)
,
4
√
3
,
(
−
4
√
3
)
(ii)
6
,
0
,
√
5
,
(
−
√
5
)
(iii)
2
,
(
−
4
)
,
3
,
(
−
3
)
(iv)
3
,
(
−
3
)
,
√
3
,
(
−
√
3
)
(v)
0
,
(
−
5
)
,
√
1
3
,
(
−
1
)
Question
5
5.
Solve :
(
x
−
2
)
(
x
−
1
)
x
(
x
+
1
)
=
840
(i)
3
,
(
−
7
)
(ii)
5
,
(
−
6
)
(iii)
7
,
(
−
4
)
(iv)
6
,
(
−
5
)
(v)
8
,
(
−
3
)
Question
6
6.
Solve the quadratic equation
x
−
5
=
6
x
(i)
(
7
,
-2
)
(ii)
(
6
,
-1
)
(iii)
(
9
,
-2
)
(iv)
(
9
,
-4
)
(v)
(
7
,
-1
)
Question
7
7.
For what values of
k
are the roots of
(
k
−
8
)
x
2
+
(
k
+
27
)
x
+
(
k
+
3
)
=
0
equal
(i)
(
(
−
41
5
)
,
32
)
(ii)
(
(
−
25
3
)
,
33
)
(iii)
(
(
−
41
5
)
,
33
)
(iv)
(
(
−
23
3
)
,
30
)
(v)
(
(
−
23
3
)
,
32
)
Question
8
8.
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
−
131
x
+
195
)
=
0
(ii)
(
14
x
2
−
149
x
+
255
)
=
0
(iii)
(
14
x
2
−
135
x
+
225
)
=
0
(iv)
(
28
x
2
−
263
x
+
435
)
=
0
(v)
(
10
x
2
−
97
x
+
165
)
=
0
Question
9
9.
If
7
is the root of
(
x
2
+
k
x
+
7
)
=
0
, find
k
and the other root
(i)
k
=
-8
, and the other root =
1
(ii)
k
=
-10
, and the other root =
-2
(iii)
k
=
-7
, and the other root =
2
(iv)
k
=
-9
, and the other root =
0
(v)
k
=
-6
, and the other root =
4
Question
10
10.
Find the quadratic equation whose roots are
(
3
−
3
√
3
)
and
(
3
+
3
√
3
)
(i)
(
x
2
−
8
x
−
18
)
=
0
(ii)
(
x
2
−
3
x
−
18
)
=
0
(iii)
(
x
2
−
6
x
−
18
)
=
0
(iv)
(
−
6
x
−
18
)
=
0
(v)
(
2
x
2
−
6
x
−
18
)
=
0
Question
11
11.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
−
4
)
,
(
x
+
9
)
and leaves a remainder of
-30
when divided by
(
x
+
6
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
4
,
c
=
-37
(ii)
a
=
1
,
b
=
5
,
c
=
-36
(iii)
a
=
1
,
b
=
6
,
c
=
-35
(iv)
a
=
1
,
b
=
7
,
c
=
-33
(v)
a
=
1
,
b
=
2
,
c
=
-39
Question
12
12.
Find
a
and
b
in order that
(
x
3
+
17
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
+
14
x
+
48
)
(i)
a
=
87
,
b
=
141
(ii)
a
=
93
,
b
=
146
(iii)
a
=
91
,
b
=
145
(iv)
a
=
89
,
b
=
143
(v)
a
=
90
,
b
=
144
Assignment Key
1) (iii)
2) (i)
3) (ii)
4) (iv)
5) (iv)
6) (ii)
7) (ii)
8) (iii)
9) (i)
10) (iii)
11) (ii)
12) (v)
