EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
x
+
9
)
(
x
+
1
)
=
(
4
x
+
3
)
(
2
x
+
9
)
(i)
(
-4
,
12
)
(ii)
(
-3
,
13
)
(iii)
(
3
,
-13
)
(iv)
(
-1
,
15
)
(v)
(
-6
,
10
)
Question
2
2.
Solve :
(
x
(
x
+
2
)
)
2
+
10
(
x
(
x
+
2
)
)
+
25
= 0
(i)
-3
,
-3
(ii)
(
-7
3
)
,
(
-7
3
)
(iii)
(
-5
3
)
,
(
-5
3
)
(iv)
(
-7
5
)
,
(
-7
5
)
(v)
-1
,
-1
Question
3
3.
Find the discriminant of the quadratic equation
(
x
2
−
3
x
+
9
)
=
0
(i)
-28
(ii)
-30
(iii)
-25
(iv)
-26
(v)
-27
Question
4
4.
Solve :
(
x
−
3
)
(
x
−
2
)
(
x
−
1
)
x
=
840
(i)
7
,
(
−
4
)
(ii)
4
,
(
−
6
)
(iii)
8
,
(
−
3
)
(iv)
10
,
(
−
2
)
(v)
6
,
(
−
5
)
Question
5
5.
Solve :
6
x
2
b
+
4
x
b
−
3
x
−
2
= 0
(i)
−
6
7
,
1
b
(ii)
−
4
9
,
3
2
b
(iii)
−
8
9
,
−
1
2
b
(iv)
−
2
3
,
1
2
b
(v)
−
6
11
,
1
4
b
Question
6
6.
Solve :
56
x
2
a
+
8
x
−
21
x
a
−
3
= 0
(i)
−
1
7
a
,
3
8
(ii)
1
7
a
,
5
8
(iii)
−
1
5
a
,
1
2
(iv)
−
1
9
a
,
3
10
(v)
−
3
7
a
,
1
8
Question
7
7.
Solve the quadratic equation
x
+
8
x
=
9
(i)
(
9
,
1
)
(ii)
(
9
,
0
)
(iii)
(
8
,
1
)
(iv)
(
10
,
-1
)
(v)
(
10
,
0
)
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)
(
40
x
2
−
162
x
−
1147
)
=
0
(ii)
(
32
x
2
−
132
x
−
899
)
=
0
(iii)
(
32
x
2
−
124
x
−
961
)
=
0
(iv)
(
32
x
2
−
108
x
−
899
)
=
0
(v)
(
16
x
2
−
74
x
−
527
)
=
0
Question
9
9.
Find the discriminant of the quadratic equation
(
x
2
−
4
x
+
4
)
=
0
(i)
3
(ii)
-2
(iii)
-1
(iv)
1
(v)
0
Question
10
10.
Solve :
25
x
2
+
20
x
+
5
x
b
+
4
b
= 0
(i)
−
2
5
,
b
5
(ii)
−
6
5
,
−
3
b
5
(iii)
−
4
5
,
−
b
5
(iv)
−
4
7
,
−
b
7
(v)
−
4
3
,
−
b
3
Question
11
11.
Find the quadratic equation with roots
(
(
-5
2
)
,
(
-1
9
)
)
(i)
(
9
x
2
+
46
x
+
5
)
=
0
(ii)
(
18
x
2
+
47
x
+
5
)
=
0
(iii)
(
18
x
2
+
43
x
−
5
)
=
0
(iv)
(
18
x
2
+
65
x
+
7
)
=
0
(v)
(
22
x
2
+
57
x
+
5
)
=
0
Question
12
12.
Find the quadratic equation with roots
(
-1
,
3
)
(i)
(
x
2
−
2
x
−
3
)
=
0
(ii)
(
x
2
−
9
)
=
0
(iii)
(
x
2
−
3
x
−
4
)
=
0
(iv)
(
x
2
−
5
x
−
6
)
=
0
(v)
(
x
2
−
x
−
6
)
=
0
Question
13
13.
The product of the roots of the quadratic equation
(
x
2
+
8
x
)
=
0
is
(i)
1
(ii)
0
(iii)
3
(iv)
-2
(v)
-1
Question
14
14.
Find the quadratic equation, the sum of whose roots is
5
and product is
4
(i)
(
x
2
−
5
x
+
4
)
=
0
(ii)
(
x
2
−
8
x
+
4
)
=
0
(iii)
(
x
2
−
2
x
+
4
)
=
0
(iv)
(
−
5
x
+
4
)
=
0
(v)
(
2
x
2
−
5
x
+
4
)
=
0
Question
15
15.
Find the quadratic equation with roots
(
(
-4
5
)
,
(
-4
5
)
)
(i)
(
35
x
2
+
48
x
+
16
)
=
0
(ii)
(
25
x
2
+
30
x
+
8
)
=
0
(iii)
(
25
x
2
+
40
x
+
16
)
=
0
(iv)
(
25
x
2
+
50
x
+
24
)
=
0
(v)
(
15
x
2
+
32
x
+
16
)
=
0
Question
16
16.
Solve :
6
x
2
b
2
−
a
2
x
b
−
a
4
= 0
(i)
a
2
2
b
,
−
a
2
3
b
(ii)
a
2
b
,
−
a
2
b
(iii)
3
a
2
2
b
,
a
2
3
b
(iv)
a
2
4
b
,
−
a
2
5
b
(v)
−
a
2
2
b
,
−
a
2
b
Question
17
17.
Solve :
42
x
2
b
−
7
x
b
+
30
x
−
5
= 0
(i)
1
6
,
−
5
7
b
(ii)
1
4
,
−
1
b
(iii)
−
1
6
,
−
1
b
(iv)
1
2
,
−
3
7
b
(v)
1
8
,
−
5
9
b
Question
18
18.
Find the roots of the quadratic equation correct to two decimal places
(
−
7
x
2
+
42
x
)
=
0
(i)
0.00 , 6.00
(ii)
8.00 , 4.00
(iii)
1.00 , 7.00
(iv)
2.00 , 8.00
(v)
7.00 , 5.00
Question
19
19.
For what values of
k
are the roots of
(
k
−
3
)
x
2
+
(
k
+
45
)
x
+
(
k
−
18
)
=
0
equal
(i)
(
(
−
6
)
,
66
)
(ii)
(
(
−
8
)
,
67
)
(iii)
(
(
−
9
)
,
67
)
(iv)
(
(
−
6
)
,
64
)
(v)
(
(
−
8
)
,
66
)
Question
20
20.
Solve :
(
2
x
+
3
)
(
x
+
2
)
+
(
x
−
3
)
(
x
−
2
)
=
53
21
(i)
(
4
,
(
-4
3
)
)
(ii)
(
8
,
(
-2
5
)
)
(iii)
(
3
,
(
-6
5
)
)
(iv)
(
6
,
(
-4
7
)
)
(v)
(
5
,
(
-4
5
)
)
Question
21
21.
The product of the roots of the quadratic equation
(
−
30
x
2
−
48
x
)
=
0
is
(i)
0
(ii)
-2
(iii)
-1
(iv)
3
(v)
1
Question
22
22.
Solve :
8
x
2
a
2
−
10
x
a
+
3
= 0
(i)
1
2
a
,
1
3
a
(ii)
3
2
a
,
1
a
(iii)
5
4
a
,
1
a
(iv)
1
4
a
,
0
(v)
3
4
a
,
2
4
a
Question
23
23.
Solve :
6
x
2
b
2
+
7
a
x
b
+
2
a
2
= 0
(i)
−
a
2
b
,
−
2
a
3
b
(ii)
−
2
a
3
b
,
−
2
a
b
(iii)
−
3
a
4
b
,
−
4
a
3
b
(iv)
−
2
a
5
b
,
−
2
a
5
b
(v)
−
a
4
b
,
0
Question
24
24.
Find
a
and
b
in order that
(
x
3
−
4
x
2
)
+
(
a
x
+
b
)
may be exactly divisible by
(
x
2
−
2
x
−
24
)
(i)
a
=
-20
,
b
=
48
(ii)
a
=
-23
,
b
=
45
(iii)
a
=
-18
,
b
=
51
(iv)
a
=
-21
,
b
=
47
(v)
a
=
-19
,
b
=
49
Question
25
25.
Find the discriminant of the quadratic equation
(
x
2
−
5
x
+
6
)
=
0
(i)
-2
(ii)
3
(iii)
0
(iv)
1
(v)
2
Assignment Key
1) (ii)
2) (iii)
3) (v)
4) (i)
5) (iv)
6) (i)
7) (iii)
8) (iii)
9) (v)
10) (iii)
11) (ii)
12) (i)
13) (ii)
14) (i)
15) (iii)
16) (i)
17) (i)
18) (i)
19) (iii)
20) (v)
21) (i)
22) (v)
23) (i)
24) (i)
25) (iv)
