EduSahara™ Assignment
Name : Solving some complex Quadratic Equations
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
7
x
+
1
)
(
17
x
+
1
)
=
(
19
x
+
1
)
(
45
x
+
1
)
(i)
(
0
,
2
)
(ii)
(
2
,
5
)
(iii)
(
-1
,
1
)
(iv)
(
0
,
-2
)
(v)
(
-2
,
-1
)
Question
2
2.
Solve :
(
x
−
10
)
(
x
−
2
)
+
(
x
−
11
)
(
x
−
6
)
=
43
77
(i)
(
12
,
438
109
)
(ii)
(
16
,
448
111
)
(iii)
(
10
,
4
)
(iv)
(
14
,
454
113
)
(v)
(
13
,
446
111
)
Question
3
3.
Solve :
(
x
2
−
6
x
)
2
−
11
(
x
2
−
6
x
)
+
30
=
0
(i)
(
3
+
15
)
,
(
3
−
15
)
,
(
3
+
14
)
,
(
3
−
14
)
(ii)
(
6
+
√
15
)
,
(
5
−
√
15
)
,
(
5
+
√
14
)
,
(
5
−
√
14
)
(iii)
(
3
+
√
15
)
,
(
3
−
√
15
)
,
(
3
+
√
14
)
,
(
3
−
√
14
)
(iv)
(
1
+
√
15
)
,
(
0
−
√
15
)
,
(
0
+
√
14
)
,
(
1
−
√
14
)
(v)
(
3
+
4
√
15
)
,
(
3
−
4
√
15
)
,
(
3
+
4
√
14
)
,
(
3
−
4
√
14
)
Question
4
4.
Solve :
(
x
4
−
10
x
2
+
21
)
=
0
(i)
4
√
7
,
(
−
4
√
7
)
,
4
√
3
,
(
−
4
√
3
)
(ii)
√
10
,
(
−
√
10
)
,
√
6
,
(
−
√
5
)
(iii)
√
7
,
(
−
√
7
)
,
√
3
,
(
−
√
3
)
(iv)
7
,
(
−
7
)
,
3
,
(
−
3
)
(v)
√
5
,
(
−
√
4
)
,
√
1
3
,
(
−
√
1
3
)
Question
5
5.
Solve :
(
x
−
5
)
(
x
−
4
)
(
x
−
3
)
(
x
−
2
)
=
360
(i)
5
,
(
−
4
)
(ii)
7
,
(
−
2
)
(iii)
11
,
1
(iv)
9
,
0
(v)
8
,
(
−
1
)
Question
6
6.
Solve the quadratic equation
x
+
56
x
=
−
15
(i)
(
-6
,
-9
)
(ii)
(
-4
,
-11
)
(iii)
(
-7
,
-8
)
(iv)
(
-4
,
-9
)
(v)
(
-6
,
-8
)
Question
7
7.
For what values of
k
are the roots of
(
k
−
17
)
x
2
+
(
k
+
22
)
x
+
(
k
+
38
)
=
0
equal
(i)
(
(
−
116
3
)
,
25
)
(ii)
(
(
−
196
5
)
,
25
)
(iii)
(
(
−
118
3
)
,
26
)
(iv)
(
(
−
116
3
)
,
24
)
(v)
(
(
−
196
5
)
,
26
)
Question
8
8.
If
p
and
q
are the roots of
(
x
2
+
15
x
+
56
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
56
x
2
+
839
x
+
3135
)
=
0
(ii)
(
72
x
2
+
1097
x
+
4161
)
=
0
(iii)
(
42
x
2
+
643
x
+
2451
)
=
0
(iv)
(
56
x
2
+
855
x
+
3249
)
=
0
(v)
(
56
x
2
+
869
x
+
3363
)
=
0
Question
9
9.
If
8
is the root of
(
x
2
+
k
x
+
8
)
=
0
, find
k
and the other root
(i)
k
=
-8
, and the other root =
2
(ii)
k
=
-11
, and the other root =
-2
(iii)
k
=
-7
, and the other root =
4
(iv)
k
=
-10
, and the other root =
0
(v)
k
=
-9
, and the other root =
1
Question
10
10.
Find the quadratic equation whose roots are
(
1
+
4
√
3
)
and
(
1
−
4
√
3
)
(i)
(
x
2
−
4
x
−
47
)
=
0
(ii)
(
x
2
+
x
−
47
)
=
0
(iii)
(
x
2
−
2
x
−
47
)
=
0
(iv)
(
2
x
2
−
2
x
−
47
)
=
0
(v)
(
−
2
x
−
47
)
=
0
Question
11
11.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
+
4
)
,
(
x
−
3
)
and leaves a remainder of
30
when divided by
(
x
−
6
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
-2
,
c
=
-14
(ii)
a
=
1
,
b
=
1
,
c
=
-12
(iii)
a
=
1
,
b
=
0
,
c
=
-13
(iv)
a
=
1
,
b
=
3
,
c
=
-9
(v)
a
=
1
,
b
=
2
,
c
=
-11
Question
12
12.
Find
a
and
b
in order that
(
x
3
−
5
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
−
9
x
+
20
)
(i)
a
=
-16
,
b
=
80
(ii)
a
=
-17
,
b
=
79
(iii)
a
=
-19
,
b
=
78
(iv)
a
=
-15
,
b
=
81
(v)
a
=
-14
,
b
=
82
Assignment Key
1) (i)
2) (v)
3) (iii)
4) (iii)
5) (v)
6) (iii)
7) (iii)
8) (iv)
9) (v)
10) (iii)
11) (ii)
12) (i)
