EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Solve :
−
1
(
−
x
−
5
)
+
3
(
−
x
+
2
)
=
−
5
(
x
−
1
)
(i)
√
33
,
(
−
√
33
)
(ii)
√
55
,
(
−
√
55
)
(iii)
√
22
,
(
−
√
22
)
(iv)
√
11
,
(
−
√
11
)
(v)
√
44
,
(
−
√
44
)
Question
2
2.
Find the roots of the quadratic equation
(
30
x
2
+
13
x
−
10
)
=
0
(i)
(
2
5
,
(
-5
6
)
)
(ii)
(
4
5
,
(
-7
6
)
)
(iii)
(
2
7
,
(
-5
4
)
)
(iv)
(
4
5
,
(
-5
4
)
)
(v)
(
2
7
,
(
-5
6
)
)
Question
3
3.
The product of the roots of the quadratic equation
(
x
2
+
12
x
+
35
)
=
0
is
(i)
33
(ii)
36
(iii)
34
(iv)
38
(v)
35
Question
4
4.
Solve :
36
x
2
b
2
+
37
a
x
b
+
7
a
2
= 0
(i)
−
a
b
,
−
3
a
4
b
(ii)
−
7
a
9
b
,
−
a
4
b
(iii)
−
5
a
9
b
,
a
4
b
(iv)
−
7
a
11
b
,
−
a
6
b
(v)
−
a
b
,
−
a
2
b
Question
5
5.
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)
22
(iii)
25
(iv)
23
(v)
24
Question
6
6.
Factorize
(
x
2
−
16
)
(i)
(
x
−
8
)
(
x
+
2
)
(ii)
(
x
+
4
)
(
x
−
4
)
(iii)
(
x
+
4
)
(
x
+
4
)
(iv)
(
x
−
4
)
(
x
−
4
)
(v)
(
x
+
8
)
(
x
−
2
)
Question
7
7.
Solve :
(
x
2
−
9
x
)
2
−
15
(
x
2
−
9
x
)
+
56
=
0
(i)
(
9
2
+
1
2
√
113
)
,
(
9
2
−
1
2
√
113
)
,
(
9
2
+
1
2
√
109
)
,
(
9
2
−
1
2
√
109
)
(ii)
(
11
2
+
1
2
√
113
)
,
(
11
2
−
1
2
√
113
)
,
(
11
2
+
1
2
√
109
)
,
(
11
2
−
1
2
√
109
)
(iii)
(
9
2
+
1
2
4
√
113
)
,
(
9
2
−
1
2
4
√
113
)
,
(
9
2
+
1
2
4
√
109
)
,
(
9
2
−
1
2
4
√
109
)
(iv)
(
7
2
+
1
2
√
113
)
,
(
7
2
−
1
2
√
113
)
,
(
7
2
+
1
2
√
109
)
,
(
7
2
−
1
2
√
109
)
(v)
(
9
2
+
113
2
)
,
(
9
2
−
113
2
)
,
(
9
2
+
109
2
)
,
(
9
2
−
109
2
)
Question
8
8.
Solve :
14
x
2
+
12
x
−
7
x
b
−
6
b
= 0
(i)
−
6
5
,
b
(ii)
−
2
3
,
b
4
(iii)
−
4
7
,
3
b
2
(iv)
−
6
7
,
b
2
(v)
−
8
7
,
−
b
2
Question
9
9.
Find the number which exceeds its reciprocal by
5
5
6
(i)
7
(ii)
4
(iii)
6
(iv)
8
(v)
5
Question
10
10.
Find the discriminant of the quadratic equation
(
x
2
−
2
x
−
8
)
=
0
(i)
39
(ii)
36
(iii)
34
(iv)
35
(v)
37
Question
11
11.
For what values of
k
are the roots of
(
k
+
48
)
x
2
+
(
k
+
13
)
x
+
k
=
0
equal
(i)
(
(
−
281
5
)
,
0
)
(ii)
(
(
−
167
3
)
,
(
−
2
)
)
(iii)
(
(
−
281
5
)
,
1
)
(iv)
(
(
−
167
3
)
,
0
)
(v)
(
(
−
169
3
)
,
1
)
Question
12
12.
Solve :
40
x
2
+
11
a
2
b
x
−
21
a
4
b
2
= 0
(i)
a
2
b
,
−
5
a
2
b
8
(ii)
a
2
b
5
,
−
9
a
2
b
8
(iii)
a
2
b
,
−
7
a
2
b
6
(iv)
3
a
2
b
5
,
−
7
a
2
b
8
(v)
3
a
2
b
7
,
−
7
a
2
b
10
Question
13
13.
A play field is
90.00 m
by
70.00 m
.
It has a road all around it on the outside.
Find the width of the road if its area is
13
12
of the area of the play field
(i)
17.50 m
(ii)
15.50 m
(iii)
16.50 m
(iv)
18.50 m
(v)
19.50 m
Question
14
14.
Find the number which is less than its square by 306
(i)
18
(ii)
15
(iii)
19
(iv)
17
(v)
21
Question
15
15.
Solve :
12
x
2
+
5
a
b
2
x
−
3
a
2
b
4
= 0
(i)
2
a
b
2
6
,
−
3
a
b
2
4
(ii)
0
,
−
5
a
b
2
4
(iii)
2
a
b
2
3
,
−
a
b
2
4
(iv)
a
b
2
4
,
−
a
b
2
2
(v)
a
b
2
2
,
−
3
a
b
2
2
Question
16
16.
Solve :
40
x
2
b
−
32
x
b
−
15
x
+
12
= 0
(i)
4
7
,
3
10
b
(ii)
4
3
,
1
2
b
(iii)
6
5
,
5
8
b
(iv)
2
5
,
1
8
b
(v)
4
5
,
3
8
b
Question
17
17.
A can do a work in
x
days and B can do it in
(
x
−
7
)
days.
Both of them working together can do it in
8
2
5
days. Calculate
x
(i)
18
(ii)
20
(iii)
24
(iv)
22
(v)
21
Question
18
18.
Solve :
35
x
2
a
2
−
12
x
a
+
1
= 0
(i)
1
3
a
,
1
5
a
(ii)
−
1
5
a
,
−
1
7
a
(iii)
3
5
a
,
3
7
a
(iv)
1
5
a
,
1
7
a
(v)
1
7
a
,
1
9
a
Question
19
19.
The sum of the numerator and denominator of a fraction is
38
.
If
2
is added to both the numerator and denominator,
the fraction is increased by
8
483
. Find the fraction
(i)
5
7
(ii)
21
17
(iii)
17
19
(iv)
19
21
(v)
17
21
Question
20
20.
Solve :
−
9
√
6
x
2
−
24
x
−
2
√
6
=
0
(i)
√
6
(
−
9
)
,
(
−
2
)
√
24
(ii)
√
24
(
−
9
)
,
(
−
2
√
4
)
√
6
(iii)
√
24
(
−
9
)
,
(
−
2
)
√
6
(iv)
√
6
(
−
9
√
4
)
,
(
−
2
)
√
24
(v)
√
6
(
−
9
)
,
(
−
2
)
√
6
Question
21
21.
Solve :
12
x
2
+
7
b
x
+
b
2
= 0
(i)
−
3
b
7
,
−
b
2
(ii)
−
b
3
,
−
b
4
(iii)
−
5
b
9
,
−
3
b
4
(iv)
−
b
9
,
b
4
(v)
−
3
b
11
,
−
b
6
Question
22
22.
The sum of the squares of two consecutive even numbers is 340. Find the numbers
(i)
12
,
14
or
(-12)
,
(-14)
(ii)
13
,
15
or
(-13)
,
(-15)
(iii)
10
,
11
or
(-10)
,
(-11)
(iv)
15
,
16
or
(-15)
,
(-16)
(v)
11
,
13
or
(-11)
,
(-13)
Question
23
23.
Find the quadratic equation with roots
(
(
-1
2
)
,
(
-1
2
)
)
(i)
(
8
x
2
+
6
x
+
1
)
=
0
(ii)
(
4
x
2
+
8
x
+
3
)
=
0
(iii)
(
4
x
2
+
4
x
+
1
)
=
0
(iv)
(
4
x
2
−
1
)
=
0
(v)
(
2
x
2
+
3
x
+
1
)
=
0
Question
24
24.
A two digit number is such that the product of the digits is 28. When 27 is subtracted from the number, the digits are reversed. Find the number
(i)
75
(ii)
77
(iii)
72
(iv)
73
(v)
74
Question
25
25.
Solve :
(
2
x
+
1
)
(
6
x
+
1
)
+
(
x
+
1
)
(
5
x
+
1
)
=
94
143
(i)
(
(
-26
133
)
,
-1
)
(ii)
(
(
-24
131
)
,
1
)
(iii)
(
(
-8
45
)
,
3
)
(iv)
(
(
-22
133
)
,
4
)
(v)
(
(
-24
133
)
,
2
)
Assignment Key
1) (iv)
2) (i)
3) (v)
4) (ii)
5) (v)
6) (ii)
7) (i)
8) (iv)
9) (iii)
10) (ii)
11) (v)
12) (iv)
13) (i)
14) (i)
15) (i)
16) (v)
17) (v)
18) (iv)
19) (v)
20) (v)
21) (ii)
22) (i)
23) (iii)
24) (v)
25) (v)
