EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Solve :
8
x
2
b
2
+
2
a
x
b
−
a
2
= 0
(i)
a
2
b
,
a
2
b
(ii)
−
a
b
,
a
3
b
(iii)
−
a
2
b
,
2
a
8
b
(iv)
−
3
a
2
b
,
0
(v)
−
a
4
b
,
a
5
b
Question
2
2.
The denominator of a fraction exceeds the numerator by
9
.
The square of the fraction is equal to
196
529
. Find the fraction
(i)
14
25
(ii)
12
23
(iii)
14
23
(iv)
16
23
(v)
2
3
Question
3
3.
The sum of the squares of two consecutive even numbers is 4. Find the numbers
(i)
(-2)
,
0
or
2
,
0
(ii)
(-4)
,
(-3)
or
4
,
3
(iii)
(-3)
,
(-1)
or
3
,
1
(iv)
0
,
3
or
0
,
(-3)
(v)
(-1)
,
1
or
1
,
(-1)
Question
4
4.
Find the roots of the quadratic equation
(
14
x
2
−
16
x
+
2
)
=
0
(i)
(
4
,
1
5
)
(ii)
(
2
,
1
5
)
(iii)
(
1
,
1
7
)
(iv)
(
4
,
(
-1
7
)
)
(v)
(
2
,
1
7
)
Question
5
5.
Find the discriminant of the quadratic equation
(
−
3
x
2
−
4
x
+
15
)
=
0
(i)
199
(ii)
193
(iii)
197
(iv)
196
(v)
195
Question
6
6.
Find the roots of the quadratic equation
(
4
x
2
−
6
x
−
3
)
=
0
(i)
(
(
3
4
+
1
4
4
√
21
)
,
(
3
4
−
21
4
)
)
(ii)
(
(
3
4
+
1
4
4
√
21
)
,
(
3
4
−
1
4
√
21
)
)
(iii)
(
(
5
4
+
1
4
√
21
)
,
(
3
4
−
21
4
)
)
(iv)
(
(
5
4
+
1
4
√
21
)
,
(
1
4
−
1
4
√
21
)
)
(v)
(
(
3
4
+
1
4
√
21
)
,
(
3
4
−
1
4
√
21
)
)
Question
7
7.
A two digit number is such that the product of the digits is 7. When 54 is subtracted from the number, the digits are reversed. Find the number
(i)
70
(ii)
72
(iii)
71
(iv)
68
(v)
73
Question
8
8.
If
9
is the root of
(
x
2
+
k
x
+
54
)
=
0
, find
k
and the other root
(i)
k
=
-18
, and the other root =
4
(ii)
k
=
-14
, and the other root =
7
(iii)
k
=
-13
, and the other root =
8
(iv)
k
=
-15
, and the other root =
6
(v)
k
=
-16
, and the other root =
5
Question
9
9.
Solve :
√
(
−
5
x
−
8
)
=
(
x
+
3
)
(i)
(
−
11
2
√
4
+
1
2
√
53
)
,
(
−
11
2
√
4
−
1
2
√
53
)
(ii)
(
−
11
2
+
1
2
√
53
)
,
(
−
11
2
−
1
2
√
53
)
(iii)
(
−
11
2
√
5
+
1
2
√
53
)
,
(
−
11
2
√
5
−
1
2
√
53
)
(iv)
(
−
11
2
+
1
2
√
106
)
,
(
−
11
2
−
1
2
√
106
)
(v)
(
−
11
2
+
1
2
√
159
)
,
(
−
11
2
−
1
2
√
159
)
Question
10
10.
Solve the quadratic equation
x
+
12
x
=
8
(i)
(
9
,
-1
)
(ii)
(
6
,
2
)
(iii)
(
7
,
1
)
(iv)
(
7
,
2
)
(v)
(
9
,
1
)
Question
11
11.
Solve :
30
x
2
−
7
a
2
b
x
−
2
a
4
b
2
= 0
(i)
2
a
2
b
7
,
−
a
2
b
8
(ii)
2
a
2
b
5
,
−
a
2
b
6
(iii)
4
a
2
b
5
,
a
2
b
6
(iv)
2
a
2
b
3
,
−
a
2
b
4
(v)
0
,
−
a
2
b
2
Question
12
12.
Find the roots of the quadratic equation
(
x
2
−
8
x
+
7
)
=
0
(i)
(
10
,
-2
)
(ii)
(
8
,
0
)
(iii)
(
7
,
1
)
(iv)
(
8
,
1
)
(v)
(
10
,
0
)
Question
13
13.
Find the discriminant of the quadratic equation
(
8
x
2
−
26
x
+
49
)
=
0
(i)
-894
(ii)
-892
(iii)
-891
(iv)
-889
(v)
-893
Question
14
14.
Solve :
6
x
2
−
b
x
−
b
2
= 0
(i)
2
b
4
,
−
b
3
(ii)
b
3
,
−
b
5
(iii)
b
,
−
b
(iv)
0
,
−
b
(v)
b
,
b
3
Question
15
15.
In a two digit number, the unit's digit exceeds it ten's digit by 1 and the product of the given number and the sum of its digits is equal to 115 . Find the number
(i)
56
(ii)
23
(iii)
12
(iv)
34
(v)
45
Question
16
16.
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 (-6) . Find the number
(i)
27
(ii)
24
(iii)
21
(iv)
25
(v)
23
Question
17
17.
Solve :
(
x
4
−
14
x
2
+
49
)
=
0
(i)
√
7
,
(
−
√
7
)
,
√
7
,
(
−
√
7
)
(ii)
4
√
7
,
(
−
4
√
7
)
,
4
√
7
,
(
−
4
√
7
)
(iii)
√
4
,
(
−
√
5
)
,
√
5
,
(
−
√
5
)
(iv)
√
9
,
(
−
√
10
)
,
√
9
,
(
−
√
10
)
(v)
7
,
(
−
7
)
,
7
,
(
−
7
)
Question
18
18.
A can do a work in
x
days and B can do it in
(
x
+
19
)
days.
Both of them working together can do it in
19
55
83
days. Calculate
x
(i)
32
(ii)
31
(iii)
35
(iv)
29
(v)
33
Question
19
19.
Solve :
6
x
2
a
2
−
x
a
−
1
= 0
(i)
2
5
a
,
−
3
11
a
(ii)
4
8
a
,
−
1
3
a
(iii)
2
3
a
,
−
3
7
a
(iv)
3
4
a
,
−
1
9
a
(v)
1
4
a
,
−
5
9
a
Question
20
20.
85 is divided into two parts such that the sum of their reciprocals is
85
1764
.
Find the two parts
(i)
(
34
,
51
)
(ii)
(
37
,
48
)
(iii)
(
36
,
49
)
(iv)
(
35
,
50
)
(v)
(
38
,
47
)
Question
21
21.
Solve :
56
x
2
+
53
a
b
x
+
12
a
2
b
2
= 0
(i)
−
6
a
b
7
,
−
5
a
b
8
(ii)
−
4
a
b
9
,
−
3
a
b
10
(iii)
−
2
a
b
7
,
−
a
b
8
(iv)
−
4
a
b
5
,
−
a
b
2
(v)
−
4
a
b
7
,
−
3
a
b
8
Question
22
22.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 320 . Find the three numbers.
(i)
20, 21, 22
(ii)
17, 18, 19
(iii)
18, 19, 20
(iv)
22, 23, 24
(v)
19, 20, 21
Question
23
23.
Solve :
(
x
+
1
)
(
x
−
7
)
=
(
2
x
+
9
)
(
x
+
2
)
(i)
(
-5
,
13
)
(ii)
(
-7
,
11
)
(iii)
(
-6
,
12
)
(iv)
(
-2
,
15
)
(v)
(
5
,
-13
)
Question
24
24.
The area of a rectangular room is 84.00 sq.m. If the length and breadth are increased by 6 m, the area would become 270.00 sq.m. Find the original dimensions of the room
(i)
3.00 m , 28.00 m
(ii)
2.00 m , 42.00 m
(iii)
5.00 m , 16.80 m
(iv)
6.00 m , 14.00 m
(v)
4.00 m , 21.00 m
Question
25
25.
One pipe can fill a cistern in
9
hours less than the other.
The two pipes together can fill it in
3
13
19
hrs.
Find the time that each pipe will take to fill the cistern.
(i)
5 hr , 14 hr
(ii)
4 hr , 13 hr
(iii)
3 hr , 11 hr
(iv)
6 hr , 15 hr
(v)
8 hr , 17 hr
Assignment Key
1) (iii)
2) (iii)
3) (i)
4) (iii)
5) (iv)
6) (v)
7) (iii)
8) (iv)
9) (ii)
10) (ii)
11) (ii)
12) (iii)
13) (ii)
14) (i)
15) (ii)
16) (ii)
17) (i)
18) (i)
19) (ii)
20) (iii)
21) (v)
22) (v)
23) (i)
24) (v)
25) (i)
