EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The area of a rectangular room is 192.00 sq.m. If the length and breadth are increased by 2 m, the area would become 300.00 sq.m. Find the original dimensions of the room
(i)
3.00 m , 64.00 m
(ii)
48.00 m , 4.00 m
(iii)
2.00 m , 96.00 m
(iv)
6.00 m , 32.00 m
(v)
5.00 m , 38.40 m
Question
2
2.
If
6
is the root of
(
x
2
+
k
x
+
18
)
=
0
, find
k
and the other root
(i)
k
=
-7
, and the other root =
5
(ii)
k
=
-9
, and the other root =
3
(iii)
k
=
-12
, and the other root =
0
(iv)
k
=
-10
, and the other root =
2
(v)
k
=
-8
, and the other root =
4
Question
3
3.
Solve :
63
x
2
a
4
b
2
+
73
x
a
2
b
+
20
= 0
(i)
−
5
7
a
2
b
,
−
4
9
a
2
b
(ii)
−
1
a
2
b
,
−
4
7
a
2
b
(iii)
−
5
9
a
2
b
,
−
4
11
a
2
b
(iv)
−
1
a
2
b
,
−
2
3
a
2
b
(v)
−
3
7
a
2
b
,
−
2
9
a
2
b
Question
4
4.
Find the roots of the quadratic equation
(
14
x
2
+
6
x
)
=
0
(i)
(
3
,
(
-5
7
)
)
(ii)
(
1
,
(
-3
7
)
)
(iii)
(
3
,
(
-3
5
)
)
(iv)
(
1
,
(
-3
5
)
)
(v)
(
0
,
(
-3
7
)
)
Question
5
5.
Find the roots of the quadratic equation
(
x
2
−
14
x
+
45
)
=
0
(i)
(
11
,
4
)
(ii)
(
9
,
5
)
(iii)
(
10
,
5
)
(iv)
(
10
,
4
)
(v)
(
11
,
2
)
Question
6
6.
The sum of the ages of a father and his son is 60 years whereas five years ago, the product of their ages was 336. Find the current ages of the son and the father.
(i)
11 years , 49 years
(ii)
14 years , 46 years
(iii)
13 years , 47 years
(iv)
12 years , 48 years
(v)
15 years , 45 years
Question
7
7.
Solve :
√
(
2
x
2
−
12
x
−
54
)
=
(
x
+
5
)
(i)
(
11
√
5
−
10
√
2
)
,
(
11
√
5
+
10
√
2
)
(ii)
(
11
−
10
√
2
)
,
(
11
+
10
√
2
)
(iii)
(
11
√
4
−
10
√
2
)
,
(
11
√
4
+
10
√
2
)
(iv)
(
11
−
20
)
,
(
11
+
20
)
(v)
(
11
−
10
√
6
)
,
(
11
+
10
√
6
)
Question
8
8.
A number is of two digits. The digit in unit's place is the square of the digit in ten's place. The number formed by reversing the digits exceeds twice the number by 15 . Find the number
(i)
40
(ii)
39
(iii)
38
(iv)
42
(v)
36
Question
9
9.
Find the roots of the quadratic equation
(
−
2
x
2
+
8
x
+
7
)
=
0
(i)
(
(
5
−
1
2
√
30
)
,
(
2
+
15
)
)
(ii)
(
(
5
−
1
2
√
30
)
,
(
0
+
1
2
√
30
)
)
(iii)
(
(
2
−
1
2
4
√
30
)
,
(
2
+
15
)
)
(iv)
(
(
2
−
1
2
4
√
30
)
,
(
2
+
1
2
√
30
)
)
(v)
(
(
2
−
1
2
√
30
)
,
(
2
+
1
2
√
30
)
)
Question
10
10.
Find the number which is less than its square by 132
(i)
12
(ii)
14
(iii)
11
(iv)
9
(v)
13
Question
11
11.
Solve :
(
7
x
+
6
)
(
x
+
3
)
=
(
20
x
+
3
)
(
3
x
+
5
)
(i)
(
-7
,
-3
)
(ii)
(
6
,
2
)
(iii)
(
9
,
6
)
(iv)
(
4
,
0
)
(v)
(
7
,
3
)
Question
12
12.
Solve :
24
x
2
b
2
−
13
x
b
−
2
= 0
(i)
2
b
,
−
1
6
b
(ii)
2
5
b
,
−
1
10
b
(iii)
4
3
b
,
1
8
b
(iv)
2
3
b
,
−
1
8
b
(v)
0
,
−
3
8
b
Question
13
13.
A can do a work in
x
days and B can do it in
(
x
−
5
)
days.
Both of them working together can do it in
10
4
41
days. Calculate
x
(i)
21
(ii)
23
(iii)
26
(iv)
22
(v)
24
Question
14
14.
Solve :
14
x
2
−
19
a
2
b
x
+
6
a
4
b
2
= 0
(i)
3
a
2
b
6
,
6
a
2
b
7
(ii)
5
a
2
b
6
,
8
a
2
b
7
(iii)
3
a
2
b
8
,
2
a
2
b
3
(iv)
3
a
2
b
4
,
6
a
2
b
5
(v)
a
2
b
6
,
4
a
2
b
7
Question
15
15.
71 is divided into two parts such that the sum of their reciprocals is
71
1170
.
Find the two parts
(i)
(
28
,
43
)
(ii)
(
27
,
44
)
(iii)
(
24
,
47
)
(iv)
(
26
,
45
)
(v)
(
25
,
46
)
Question
16
16.
Solve :
48
x
2
−
14
√
6
x
+
6
=
0
(i)
√
6
8
,
√
6
6
(ii)
√
6
8
,
√
6
6
√
4
(iii)
√
24
8
,
√
6
6
(iv)
√
6
8
√
4
,
√
6
6
√
4
(v)
√
24
8
,
√
24
6
Question
17
17.
Solve the quadratic equation
x
+
14
x
=
9
(i)
(
10
,
0
)
(ii)
(
7
,
2
)
(iii)
(
8
,
1
)
(iv)
(
8
,
2
)
(v)
(
10
,
1
)
Question
18
18.
Solve :
54
x
2
b
2
−
15
a
x
b
+
a
2
= 0
(i)
a
2
b
,
a
3
b
(ii)
a
6
b
,
a
9
b
(iii)
−
a
6
b
,
−
a
9
b
(iv)
a
8
b
,
a
11
b
(v)
a
4
b
,
a
7
b
Question
19
19.
Solve :
√
(
−
4
x
−
4
)
=
(
x
+
2
)
(i)
(
−
4
+
2
√
2
)
,
(
−
4
−
2
√
2
)
(ii)
(
−
4
√
5
+
2
√
2
)
,
(
−
4
√
5
−
2
√
2
)
(iii)
(
−
4
+
4
)
,
(
−
4
−
4
)
(iv)
(
−
4
+
2
√
6
)
,
(
−
4
−
2
√
6
)
(v)
(
−
4
√
4
+
2
√
2
)
,
(
−
4
√
4
−
2
√
2
)
Question
20
20.
The sum of the squares of two consecutive odd numbers is 290. Find the numbers
(i)
(-13)
,
(-11)
or
13
,
11
(ii)
(-12)
,
(-10)
or
12
,
10
(iii)
(-16)
,
(-14)
or
16
,
14
(iv)
(-11)
,
(-8)
or
11
,
8
(v)
(-14)
,
(-12)
or
14
,
12
Question
21
21.
A two digit number is such that the product of the digits is 9. When 72 is subtracted from the number, the digits are reversed. Find the number
(i)
94
(ii)
91
(iii)
90
(iv)
92
(v)
88
Question
22
22.
Solve :
28
x
2
a
4
+
17
b
x
a
2
−
6
b
2
= 0
(i)
−
b
4
a
2
,
−
8
b
7
a
2
(ii)
b
2
a
2
,
−
6
b
5
a
2
(iii)
b
4
a
2
,
−
6
b
7
a
2
(iv)
3
b
4
a
2
,
−
4
b
7
a
2
(v)
b
6
a
2
,
−
2
b
3
a
2
Question
23
23.
The perimeter of a rectangular room is 38.00 m and the length of its diagonal is 13.89 m . Find the dimensions of the room
(i)
12.00 m , 7.00 m
(ii)
14.00 m , 5.00 m
(iii)
13.00 m , 6.00 m
(iv)
11.00 m , 8.00 m
(v)
10.00 m , 9.00 m
Question
24
24.
Solve :
6
x
2
−
√
6
x
−
12
=
0
(i)
(
−
3
)
√
24
,
4
√
24
(ii)
(
−
3
√
4
)
√
6
,
4
√
6
(iii)
(
−
3
)
√
6
,
4
√
24
(iv)
(
−
3
)
√
6
,
4
√
6
(v)
(
−
3
√
4
)
√
6
,
4
√
4
√
6
Question
25
25.
If the difference of two numbers is 6 and their product is -5, find the numbers
(i)
2
,
(-4)
or
(-2)
,
4
(ii)
0
,
(-6)
or
0
,
6
(iii)
1
,
(-5)
or
(-1)
,
5
(iv)
(-1)
,
(-8)
or
1
,
8
(v)
4
,
(-2)
or
(-4)
,
2
Assignment Key
1) (ii)
2) (ii)
3) (i)
4) (v)
5) (ii)
6) (iii)
7) (ii)
8) (ii)
9) (v)
10) (i)
11) (v)
12) (iv)
13) (ii)
14) (i)
15) (iv)
16) (i)
17) (ii)
18) (ii)
19) (i)
20) (i)
21) (ii)
22) (iii)
23) (i)
24) (iv)
25) (iii)
