EduSahara™ Assignment
Name : Solving some complex Quadratic Equations
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
4
x
+
1
)
(
18
x
+
1
)
=
(
6
x
+
3
)
(
28
x
+
3
)
(i)
(
8
,
3
)
(ii)
(
5
,
0
)
(iii)
(
3
,
-2
)
(iv)
(
-5
,
0
)
(v)
(
4
,
-1
)
Question
2
2.
Solve :
(
4
x
+
1
)
(
x
−
1
)
+
(
3
x
+
2
)
(
x
+
2
)
=
87
10
(i)
(
(
-52
15
)
,
2
)
(ii)
(
(
-60
17
)
,
1
)
(iii)
(
(
-58
17
)
,
3
)
(iv)
(
(
-64
19
)
,
4
)
(v)
(
(
-56
17
)
,
6
)
Question
3
3.
Solve :
(
x
2
−
7
x
)
2
−
8
(
x
2
−
7
x
)
+
16
=
0
(i)
(
9
2
+
1
2
√
65
)
,
(
9
2
−
1
2
√
65
)
,
(
9
2
+
1
2
√
65
)
,
(
9
2
−
1
2
√
65
)
(ii)
(
7
2
+
1
2
√
65
)
,
(
7
2
−
1
2
√
65
)
,
(
7
2
+
1
2
√
65
)
,
(
7
2
−
1
2
√
65
)
(iii)
(
7
2
+
65
2
)
,
(
7
2
−
65
2
)
,
(
7
2
+
65
2
)
,
(
7
2
−
65
2
)
(iv)
(
7
2
+
1
2
4
√
65
)
,
(
7
2
−
1
2
4
√
65
)
,
(
7
2
+
1
2
4
√
65
)
,
(
7
2
−
1
2
4
√
65
)
(v)
(
5
2
+
1
2
√
65
)
,
(
5
2
−
1
2
√
65
)
,
(
5
2
+
1
2
√
65
)
,
(
5
2
−
1
2
√
65
)
Question
4
4.
Solve :
(
x
4
−
9
x
2
+
14
)
=
0
(i)
√
9
,
(
−
√
10
)
,
√
5
,
(
−
√
5
)
(ii)
√
7
,
(
−
√
7
)
,
√
2
,
(
−
√
2
)
(iii)
4
√
7
,
(
−
4
√
7
)
,
4
√
2
,
(
−
4
√
2
)
(iv)
√
4
,
(
−
√
4
)
,
√
-1
,
(
−
√
1
2
)
(v)
7
,
(
−
7
)
,
2
,
(
−
2
)
Question
5
5.
Solve :
(
x
+
7
)
(
x
+
8
)
(
x
+
9
)
(
x
+
10
)
=
7920
(i)
(
−
2
)
,
(
−
20
)
(ii)
2
,
(
−
17
)
(iii)
0
,
(
−
19
)
(iv)
4
,
(
−
16
)
(v)
1
,
(
−
18
)
Question
6
6.
Solve the quadratic equation
x
+
15
=
−
56
x
(i)
(
-4
,
-11
)
(ii)
(
-6
,
-9
)
(iii)
(
-6
,
-8
)
(iv)
(
-7
,
-8
)
(v)
(
-4
,
-9
)
Question
7
7.
For what values of
k
are the roots of
(
k
+
14
)
x
2
+
(
k
−
1
)
x
+
(
k
−
10
)
=
0
equal
(i)
(
(
−
16
)
,
10
)
(ii)
(
(
−
15
)
,
8
)
(iii)
(
(
−
17
)
,
11
)
(iv)
(
(
−
15
)
,
10
)
(v)
(
(
−
16
)
,
11
)
Question
8
8.
If
p
and
q
are the roots of
(
x
2
+
17
x
+
72
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
56
x
2
+
967
x
+
4161
)
=
0
(ii)
(
24
x
2
+
419
x
+
1825
)
=
0
(iii)
(
72
x
2
+
1223
x
+
5183
)
=
0
(iv)
(
90
x
2
+
1549
x
+
6643
)
=
0
(v)
(
72
x
2
+
1241
x
+
5329
)
=
0
Question
9
9.
If
6
is the root of
(
x
2
+
k
x
−
18
)
=
0
, find
k
and the other root
(i)
k
=
-1
, and the other root =
-1
(ii)
k
=
-2
, and the other root =
-2
(iii)
k
=
-4
, and the other root =
-4
(iv)
k
=
-5
, and the other root =
-5
(v)
k
=
-3
, and the other root =
-3
Question
10
10.
Find the quadratic equation whose roots are
(
4
−
4
√
6
)
and
(
4
+
4
√
6
)
(i)
(
−
8
x
−
80
)
=
0
(ii)
(
x
2
−
5
x
−
80
)
=
0
(iii)
(
x
2
−
8
x
−
80
)
=
0
(iv)
(
x
2
−
11
x
−
80
)
=
0
(v)
(
2
x
2
−
8
x
−
80
)
=
0
Question
11
11.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
−
1
)
,
(
x
+
1
)
and leaves a remainder of
48
when divided by
(
x
−
7
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
1
,
c
=
0
(ii)
a
=
1
,
b
=
-1
,
c
=
-2
(iii)
a
=
1
,
b
=
-2
,
c
=
-4
(iv)
a
=
1
,
b
=
0
,
c
=
-1
(v)
a
=
1
,
b
=
2
,
c
=
1
Question
12
12.
Find
a
and
b
in order that
(
x
3
−
13
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
−
7
x
−
8
)
(i)
a
=
34
,
b
=
48
(ii)
a
=
33
,
b
=
47
(iii)
a
=
37
,
b
=
51
(iv)
a
=
35
,
b
=
49
(v)
a
=
32
,
b
=
45
Assignment Key
1) (ii)
2) (iii)
3) (ii)
4) (ii)
5) (v)
6) (iv)
7) (iii)
8) (v)
9) (v)
10) (iii)
11) (iv)
12) (i)
