EduSahara™ Assignment
Name : Solving some complex Quadratic Equations
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
x
−
7
)
(
x
−
3
)
=
(
2
x
+
7
)
(
4
x
+
3
)
(i)
(
-13
,
0
)
(ii)
(
13
,
0
)
(iii)
(
12
,
-1
)
(iv)
(
15
,
2
)
(v)
(
10
,
-3
)
Question
2
2.
Solve :
(
x
+
2
)
(
2
x
+
1
)
+
(
4
x
+
1
)
(
3
x
+
2
)
=
146
77
(i)
(
(
-29
27
)
,
2
)
(ii)
(
(
-31
29
)
,
3
)
(iii)
(
(
-33
31
)
,
4
)
(iv)
(
(
-33
29
)
,
1
)
(v)
(
-1
,
6
)
Question
3
3.
Solve :
(
x
2
−
2
x
)
2
−
11
(
x
2
−
2
x
)
+
28
=
0
(i)
(
1
+
2
4
√
2
)
,
(
1
−
2
4
√
2
)
,
(
1
+
4
√
5
)
,
(
1
−
4
√
5
)
(ii)
(
−
1
+
2
√
2
)
,
(
−
1
−
2
√
2
)
,
(
−
1
+
√
5
)
,
(
−
2
−
√
5
)
(iii)
(
1
+
2
√
2
)
,
(
1
−
2
√
2
)
,
(
1
+
√
5
)
,
(
1
−
√
5
)
(iv)
(
1
+
4
)
,
(
1
−
4
)
,
(
1
+
5
)
,
(
1
−
5
)
(v)
(
4
+
2
√
2
)
,
(
4
−
2
√
2
)
,
(
3
+
√
5
)
,
(
4
−
√
5
)
Question
4
4.
Solve :
(
x
4
−
14
x
2
+
45
)
=
0
(i)
5
,
(
−
1
)
,
√
7
,
(
−
√
7
)
(ii)
1
,
(
−
5
)
,
√
3
,
(
−
√
2
)
(iii)
3
,
(
−
3
)
,
√
5
,
(
−
√
5
)
(iv)
2
,
(
−
4
)
,
5
,
(
−
5
)
(v)
4
,
(
−
2
)
,
4
√
5
,
(
−
4
√
5
)
Question
5
5.
Solve :
(
x
+
3
)
(
x
+
4
)
(
x
+
5
)
(
x
+
6
)
=
17160
(i)
9
,
(
−
14
)
(ii)
8
,
(
−
15
)
(iii)
6
,
(
−
17
)
(iv)
4
,
(
−
19
)
(v)
7
,
(
−
16
)
Question
6
6.
Solve the quadratic equation
x
+
6
=
16
x
(i)
(
3
,
-8
)
(ii)
(
3
,
-9
)
(iii)
(
4
,
-9
)
(iv)
(
4
,
-11
)
(v)
(
2
,
-8
)
Question
7
7.
For what values of
k
are the roots of
(
k
−
21
)
x
2
+
(
k
+
39
)
x
+
(
k
+
7
)
=
0
equal
(i)
(
(
−
61
5
)
,
56
)
(ii)
(
(
−
35
3
)
,
54
)
(iii)
(
(
−
35
3
)
,
56
)
(iv)
(
(
−
61
5
)
,
57
)
(v)
(
(
−
37
3
)
,
57
)
Question
8
8.
If
p
and
q
are the roots of
(
x
2
−
4
x
−
21
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
7
x
2
−
22
x
−
120
)
=
0
(ii)
(
7
x
2
−
36
x
−
160
)
=
0
(iii)
(
21
x
2
−
86
x
−
360
)
=
0
(iv)
(
9
x
2
−
36
x
−
160
)
=
0
(v)
(
21
x
2
−
80
x
−
400
)
=
0
Question
9
9.
If
-2
is the root of
(
x
2
+
k
x
+
10
)
=
0
, find
k
and the other root
(i)
k
=
5
, and the other root =
-8
(ii)
k
=
6
, and the other root =
-6
(iii)
k
=
7
, and the other root =
-5
(iv)
k
=
9
, and the other root =
-2
(v)
k
=
8
, and the other root =
-4
Question
10
10.
Find the quadratic equation whose roots are
(
8
+
7
√
5
)
and
(
8
−
7
√
5
)
(i)
(
x
2
−
19
x
−
181
)
=
0
(ii)
(
x
2
−
13
x
−
181
)
=
0
(iii)
(
2
x
2
−
16
x
−
181
)
=
0
(iv)
(
−
16
x
−
181
)
=
0
(v)
(
x
2
−
16
x
−
181
)
=
0
Question
11
11.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
−
7
)
,
(
x
+
4
)
and leaves a remainder of
-24
when divided by
(
x
+
1
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
-2
,
c
=
-27
(ii)
a
=
1
,
b
=
-4
,
c
=
-29
(iii)
a
=
1
,
b
=
-1
,
c
=
-26
(iv)
a
=
1
,
b
=
-3
,
c
=
-28
(v)
a
=
1
,
b
=
-6
,
c
=
-31
Question
12
12.
Find
a
and
b
in order that
(
x
3
+
12
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
+
3
x
−
18
)
(i)
a
=
10
,
b
=
-161
(ii)
a
=
7
,
b
=
-165
(iii)
a
=
11
,
b
=
-160
(iv)
a
=
9
,
b
=
-162
(v)
a
=
8
,
b
=
-163
Assignment Key
1) (ii)
2) (ii)
3) (iii)
4) (iii)
5) (v)
6) (v)
7) (v)
8) (v)
9) (iii)
10) (v)
11) (iv)
12) (iv)
