EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
(
x
2
−
2
x
)
2
−
11
(
x
2
−
2
x
)
+
30
=
0
(i)
(
1
+
7
)
,
(
1
−
7
)
,
(
1
+
6
)
,
(
1
−
6
)
(ii)
(
3
+
√
7
)
,
(
4
−
√
7
)
,
(
3
+
√
6
)
,
(
4
−
√
6
)
(iii)
(
−
1
+
√
7
)
,
(
−
2
−
√
7
)
,
(
−
1
+
√
6
)
,
(
−
2
−
√
6
)
(iv)
(
1
+
√
7
)
,
(
1
−
√
7
)
,
(
1
+
√
6
)
,
(
1
−
√
6
)
(v)
(
1
+
4
√
7
)
,
(
1
−
4
√
7
)
,
(
1
+
4
√
6
)
,
(
1
−
4
√
6
)
Question
2
2.
Solve the quadratic equation
x
+
3
=
54
x
(i)
(
6
,
-9
)
(ii)
(
7
,
-9
)
(iii)
(
9
,
-10
)
(iv)
(
7
,
-10
)
(v)
(
9
,
-12
)
Question
3
3.
The product of the roots of the quadratic equation
(
49
x
2
+
56
x
+
16
)
=
0
is
(i)
16
51
(ii)
18
49
(iii)
2
7
(iv)
16
47
(v)
16
49
Question
4
4.
Solve :
6
x
2
+
5
√
6
x
+
6
=
0
(i)
(
−
2
)
√
6
,
(
−
3
)
√
24
(ii)
(
−
2
)
√
6
,
(
−
3
)
√
6
(iii)
(
−
2
)
√
24
,
(
−
3
)
√
24
(iv)
(
−
2
√
4
)
√
6
,
(
−
3
)
√
6
(v)
(
−
2
√
4
)
√
6
,
(
−
3
√
4
)
√
6
Question
5
5.
Solve :
21
x
2
b
4
−
32
a
x
b
2
+
12
a
2
= 0
(i)
2
a
b
2
,
6
a
5
b
2
(ii)
2
a
3
b
2
,
6
a
7
b
2
(iii)
4
a
3
b
2
,
8
a
7
b
2
(iv)
0
,
4
a
7
b
2
(v)
2
a
5
b
2
,
2
a
3
b
2
Question
6
6.
Solve :
40
x
2
a
4
b
2
+
19
x
a
2
b
−
3
= 0
(i)
−
1
8
a
2
b
,
−
1
a
2
b
(ii)
1
6
a
2
b
,
−
1
a
2
b
(iii)
1
10
a
2
b
,
−
3
7
a
2
b
(iv)
3
8
a
2
b
,
−
1
5
a
2
b
(v)
1
8
a
2
b
,
−
3
5
a
2
b
Question
7
7.
Find the roots of the quadratic equation correct to two decimal places
(
35
x
2
−
37
x
−
6
)
=
0
(i)
3.20 , 1.86
(ii)
9.20 , 7.86
(iii)
2.20 , 0.86
(iv)
0.20 , 6.86
(v)
1.20 , -0.14
Question
8
8.
Find the quadratic equation, the sum of whose roots is
16
and product is
64
(i)
(
x
2
−
16
x
+
64
)
=
0
(ii)
(
x
2
−
13
x
+
64
)
=
0
(iii)
(
2
x
2
−
16
x
+
64
)
=
0
(iv)
(
x
2
−
19
x
+
64
)
=
0
(v)
(
−
16
x
+
64
)
=
0
Question
9
9.
Find the quadratic equation with roots
(
1
6
,
5
9
)
(i)
(
54
x
2
−
39
x
+
5
)
=
0
(ii)
(
36
x
2
−
29
x
+
5
)
=
0
(iii)
(
66
x
2
−
41
x
+
5
)
=
0
(iv)
(
54
x
2
−
51
x
+
7
)
=
0
(v)
(
54
x
2
−
21
x
−
5
)
=
0
Question
10
10.
The product of the roots of the quadratic equation
(
x
2
+
6
x
)
=
0
is
(i)
3
(ii)
-2
(iii)
-1
(iv)
0
(v)
1
Question
11
11.
The sum of the roots of the quadratic equation
(
x
2
−
2
x
+
1
)
=
0
is
(i)
1
(ii)
4
(iii)
2
(iv)
-1
(v)
3
Question
12
12.
Find the discriminant of the quadratic equation
(
x
2
+
2
x
−
3
)
=
0
(i)
16
(ii)
15
(iii)
17
(iv)
14
(v)
19
Question
13
13.
If
a
x
2
+
b
x
+
c
is exactly divisible by
(
x
+
7
)
,
(
x
+
2
)
and leaves a remainder of
14
when divided by
(
x
+
9
)
, find
a
,
b
and
c
(i)
a
=
1
,
b
=
7
,
c
=
11
(ii)
a
=
1
,
b
=
9
,
c
=
14
(iii)
a
=
1
,
b
=
10
,
c
=
15
(iv)
a
=
1
,
b
=
8
,
c
=
13
(v)
a
=
1
,
b
=
12
,
c
=
16
Question
14
14.
Solve :
42
x
2
+
a
x
−
a
2
= 0
(i)
−
a
6
,
a
7
(ii)
a
6
,
3
a
7
(iii)
−
a
2
,
−
a
7
(iv)
−
a
4
,
a
5
(v)
−
a
8
,
a
9
Question
15
15.
Find the discriminant of the quadratic equation
(
−
3
x
2
+
4
x
)
=
0
(i)
19
(ii)
16
(iii)
17
(iv)
15
(v)
14
Question
16
16.
Find the roots of the quadratic equation
(
x
2
−
6
x
+
8
)
=
0
(i)
(
5
,
1
)
(ii)
(
5
,
2
)
(iii)
(
7
,
1
)
(iv)
(
4
,
2
)
(v)
(
7
,
-1
)
Question
17
17.
Solve :
−
2
(
x
−
3
)
+
5
(
−
x
−
3
)
=
−
3
(
x
−
5
)
(i)
9
√
3
,
2
√
3
(ii)
9
√
5
,
2
√
5
(iii)
9
,
2
(iv)
9
√
4
,
2
√
4
(v)
9
√
2
,
2
√
2
Question
18
18.
Solve :
10
x
2
b
2
+
3
a
2
x
b
−
a
4
= 0
(i)
−
a
2
b
,
a
2
3
b
(ii)
−
a
2
2
b
,
a
2
5
b
(iii)
a
2
2
b
,
3
a
2
5
b
(iv)
−
a
2
4
b
,
a
2
7
b
(v)
−
3
a
2
2
b
,
−
a
2
5
b
Question
19
19.
Solve :
(
x
(
x
−
3
)
)
2
+
5
(
x
(
x
−
3
)
)
−
24
= 0
(i)
17
4
,
12
5
(ii)
11
2
,
10
3
(iii)
7
2
,
2
(iv)
5
,
4
(v)
9
2
,
8
3
Question
20
20.
Solve :
24
x
2
b
+
8
x
b
−
15
x
−
5
= 0
(i)
−
1
3
,
5
8
b
(ii)
−
3
11
,
1
2
b
(iii)
−
1
9
,
7
8
b
(iv)
−
5
9
,
3
8
b
(v)
−
3
7
,
5
6
b
Question
21
21.
Solve :
(
x
4
−
13
x
2
+
40
)
=
0
(i)
2
4
√
2
,
(
−
2
4
√
2
)
,
4
√
5
,
(
−
4
√
5
)
(ii)
2
√
1
2
,
(
−
2
√
1
2
)
,
√
2
,
(
−
√
3
)
(iii)
4
,
(
−
4
)
,
5
,
(
−
5
)
(iv)
2
√
2
,
(
−
2
√
2
)
,
√
5
,
(
−
√
5
)
(v)
2
√
5
,
(
−
2
√
5
)
,
√
8
,
(
−
√
7
)
Question
22
22.
Find the quadratic equation, the sum of whose roots is
-2
and product is
-63
(i)
(
x
2
+
4
x
−
63
)
=
0
(ii)
(
2
x
−
63
)
=
0
(iii)
(
2
x
2
+
2
x
−
63
)
=
0
(iv)
(
x
2
+
2
x
−
63
)
=
0
(v)
(
x
2
−
63
)
=
0
Question
23
23.
If
8
is the root of
(
x
2
+
k
x
−
56
)
=
0
, find
k
and the other root
(i)
k
=
-4
, and the other root =
-9
(ii)
k
=
-1
, and the other root =
-7
(iii)
k
=
-2
, and the other root =
-8
(iv)
k
=
0
, and the other root =
-6
(v)
k
=
1
, and the other root =
-5
Question
24
24.
Find the discriminant of the quadratic equation
(
x
2
−
3
x
+
12
)
=
0
(i)
-36
(ii)
-40
(iii)
-38
(iv)
-42
(v)
-39
Question
25
25.
Find the quadratic equation, the sum of whose roots is
14
and product is
49
(i)
(
x
2
−
12
x
+
49
)
=
0
(ii)
(
−
14
x
+
49
)
=
0
(iii)
(
2
x
2
−
14
x
+
49
)
=
0
(iv)
(
x
2
−
14
x
+
49
)
=
0
(v)
(
x
2
−
16
x
+
49
)
=
0
Assignment Key
1) (iv)
2) (i)
3) (v)
4) (ii)
5) (ii)
6) (v)
7) (v)
8) (i)
9) (i)
10) (iv)
11) (iii)
12) (i)
13) (ii)
14) (i)
15) (ii)
16) (iv)
17) (iii)
18) (ii)
19) (v)
20) (i)
21) (iv)
22) (iv)
23) (ii)
24) (v)
25) (iv)
