EduSahara™ Assignment
Name : Solving some complex Quadratic Equations
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
25
x
+
2
)
(
47
x
+
2
)
=
(
11
x
+
2
)
(
21
x
+
2
)
(i)
(
2
,
-1
)
(ii)
(
6
,
2
)
(iii)
(
3
,
0
)
(iv)
(
1
,
-3
)
(v)
(
-3
,
0
)
Question
2
2.
Solve :
(
3
x
+
2
)
(
2
x
+
1
)
+
(
4
x
+
1
)
(
x
−
1
)
=
113
14
(i)
(
(
-11
24
)
,
3
)
(ii)
(
(
-3
8
)
,
6
)
(iii)
(
(
-1
2
)
,
2
)
(iv)
(
(
-11
26
)
,
4
)
(v)
(
(
-13
24
)
,
1
)
Question
3
3.
Solve :
(
x
2
−
x
)
2
−
8
(
x
2
−
x
)
+
12
=
0
(i)
3
,
(
−
2
)
,
2
,
(
−
1
)
(ii)
2
,
(
−
3
)
,
1
,
(
−
2
)
(iii)
4
,
(
−
1
)
,
3
,
0
(iv)
0
,
(
−
4
)
,
0
,
(
−
4
)
(v)
5
,
0
,
4
,
1
Question
4
4.
Solve :
(
x
4
−
17
x
2
+
72
)
=
0
(i)
4
,
(
−
2
)
,
2
4
√
2
,
(
−
2
4
√
2
)
(ii)
1
,
(
−
6
)
,
2
√
-1
,
(
−
2
√
-1
)
(iii)
5
,
(
−
1
)
,
2
√
5
,
(
−
2
√
4
)
(iv)
3
,
(
−
3
)
,
2
√
2
,
(
−
2
√
2
)
(v)
2
,
(
−
4
)
,
4
,
(
−
4
)
Question
5
5.
Solve :
(
x
+
7
)
(
x
+
8
)
(
x
+
9
)
(
x
+
10
)
=
24
(i)
(
−
4
)
,
(
−
9
)
(ii)
(
−
6
)
,
(
−
11
)
(iii)
(
−
5
)
,
(
−
10
)
(iv)
(
−
7
)
,
(
−
12
)
(v)
(
−
9
)
,
(
−
14
)
Question
6
6.
Solve the quadratic equation
x
−
27
x
=
−
6
(i)
(
5
,
-11
)
(ii)
(
4
,
-9
)
(iii)
(
3
,
-9
)
(iv)
(
5
,
-10
)
(v)
(
4
,
-10
)
Question
7
7.
For what values of
k
are the roots of
(
k
−
24
)
x
2
+
(
k
+
9
)
x
+
(
k
+
16
)
=
0
equal
(i)
(
(
−
47
3
)
,
32
)
(ii)
(
(
−
47
3
)
,
30
)
(iii)
(
(
−
81
5
)
,
33
)
(iv)
(
(
−
49
3
)
,
33
)
(v)
(
(
−
81
5
)
,
32
)
Question
8
8.
If
p
and
q
are the roots of
(
x
2
−
4
x
−
32
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
32
x
2
−
108
x
−
899
)
=
0
(ii)
(
16
x
2
−
74
x
−
527
)
=
0
(iii)
(
32
x
2
−
132
x
−
899
)
=
0
(iv)
(
32
x
2
−
124
x
−
961
)
=
0
(v)
(
40
x
2
−
162
x
−
1147
)
=
0
Question
9
9.
If
8
is the root of
(
x
2
+
k
x
−
48
)
=
0
, find
k
and the other root
(i)
k
=
-5
, and the other root =
-9
(ii)
k
=
-3
, and the other root =
-7
(iii)
k
=
-2
, and the other root =
-6
(iv)
k
=
0
, and the other root =
-4
(v)
k
=
-1
, and the other root =
-5
Question
10
10.
Find the quadratic equation whose roots are
(
2
−
6
√
2
)
and
(
2
+
6
√
2
)
(i)
(
−
4
x
−
68
)
=
0
(ii)
(
x
2
−
6
x
−
68
)
=
0
(iii)
(
2
x
2
−
4
x
−
68
)
=
0
(iv)
(
x
2
−
4
x
−
68
)
=
0
(v)
(
x
2
−
2
x
−
68
)
=
0
Question
11
11.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
−
6
)
,
(
x
−
1
)
and leaves a remainder of
150
when divided by
(
x
+
9
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
-10
,
c
=
4
(ii)
a
=
1
,
b
=
-8
,
c
=
5
(iii)
a
=
1
,
b
=
-4
,
c
=
8
(iv)
a
=
1
,
b
=
-7
,
c
=
6
(v)
a
=
1
,
b
=
-6
,
c
=
7
Question
12
12.
Find
a
and
b
in order that
(
x
3
−
3
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
−
8
x
+
7
)
(i)
a
=
-30
,
b
=
37
(ii)
a
=
-34
,
b
=
34
(iii)
a
=
-32
,
b
=
36
(iv)
a
=
-33
,
b
=
35
(v)
a
=
-35
,
b
=
32
Assignment Key
1) (iii)
2) (i)
3) (i)
4) (iv)
5) (ii)
6) (iii)
7) (iv)
8) (iv)
9) (iii)
10) (iv)
11) (iv)
12) (iv)
