EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 117 . Find the three numbers.
(i)
12, 13, 14
(ii)
13, 14, 15
(iii)
10, 11, 12
(iv)
11, 12, 13
(v)
15, 16, 17
Question
2
2.
Find the number which is less than its square by 156
(i)
10
(ii)
12
(iii)
15
(iv)
14
(v)
13
Question
3
3.
Find the quadratic equation, the sum of whose roots is
14
and product is
49
(i)
(
−
14
x
+
49
)
=
0
(ii)
(
x
2
−
12
x
+
49
)
=
0
(iii)
(
x
2
−
14
x
+
49
)
=
0
(iv)
(
2
x
2
−
14
x
+
49
)
=
0
(v)
(
x
2
−
16
x
+
49
)
=
0
Question
4
4.
A two digit number is such that the product of the digits is 36. When 45 is added to the number, the digits are reversed. Find the number
(i)
47
(ii)
52
(iii)
48
(iv)
50
(v)
49
Question
5
5.
Solve :
√
(
4
x
2
+
x
−
5
)
=
(
x
−
2
)
(i)
(
−
5
6
−
1
6
√
399
)
,
(
−
5
6
+
1
6
√
399
)
(ii)
(
−
5
6
−
1
6
√
133
)
,
(
−
5
6
+
1
6
√
133
)
(iii)
(
−
5
6
√
5
−
1
6
√
133
)
,
(
−
5
6
√
5
+
1
6
√
133
)
(iv)
(
−
5
6
√
4
−
1
6
√
133
)
,
(
−
5
6
√
4
+
1
6
√
133
)
(v)
(
−
5
6
−
1
6
√
266
)
,
(
−
5
6
+
1
6
√
266
)
Question
6
6.
Find the roots of the quadratic equation
(
−
2
x
2
+
8
x
−
4
)
=
0
(i)
(
(
4
−
√
2
)
,
(
−
1
+
√
2
)
)
(ii)
(
(
2
−
√
2
)
,
(
2
+
√
2
)
)
(iii)
(
(
4
−
√
2
)
,
(
2
+
2
)
)
(iv)
(
(
2
−
4
√
2
)
,
(
2
+
√
2
)
)
(v)
(
(
2
−
4
√
2
)
,
(
2
+
2
)
)
Question
7
7.
Solve :
9
x
2
a
2
+
12
b
2
x
a
+
4
b
4
= 0
(i)
−
b
2
a
,
−
2
b
2
a
(ii)
−
b
2
2
a
,
−
2
b
2
5
a
(iii)
−
b
2
3
a
,
0
(iv)
−
2
b
2
3
a
,
−
2
b
2
3
a
(v)
−
b
2
a
,
−
4
b
2
3
a
Question
8
8.
The perimeter of a rectangular room is 76.00 m and the length of its diagonal is 32.56 m . Find the dimensions of the room
(i)
34.00 m , 4.00 m
(ii)
30.00 m , 8.00 m
(iii)
33.00 m , 5.00 m
(iv)
32.00 m , 6.00 m
(v)
31.00 m , 7.00 m
Question
9
9.
Find the quadratic equation with roots
(
-5
,
5
)
(i)
(
x
2
−
x
−
30
)
=
0
(ii)
(
x
2
+
x
−
30
)
=
0
(iii)
(
x
2
−
25
)
=
0
(iv)
(
x
2
+
2
x
−
35
)
=
0
(v)
(
x
2
−
3
x
−
40
)
=
0
Question
10
10.
Solve :
1
(
x
+
5
)
+
2
(
−
x
−
2
)
=
−
4
(i)
(
−
5
√
4
)
,
(
−
2
√
4
)
(ii)
(
−
5
√
5
)
,
(
−
2
√
5
)
(iii)
(
−
5
)
,
(
−
2
)
(iv)
(
−
5
√
2
)
,
(
−
2
√
2
)
(v)
(
−
5
√
3
)
,
(
−
2
√
3
)
Question
11
11.
Solve :
72
x
2
−
9
x
+
16
x
b
−
2
b
= 0
(i)
−
1
8
,
−
4
b
9
(ii)
1
8
,
−
2
b
9
(iii)
1
6
,
−
2
b
7
(iv)
3
8
,
0
(v)
1
10
,
−
2
b
11
Question
12
12.
The denominator of a fraction exceeds the numerator by
1
.
The square of the fraction is equal to
100
121
. Find the fraction
(i)
10
9
(ii)
10
13
(iii)
10
11
(iv)
12
11
(v)
8
11
Question
13
13.
Find the quadratic equation, the sum of whose roots is
-2
and product is
1
(i)
(
x
2
+
5
x
+
1
)
=
0
(ii)
(
2
x
+
1
)
=
0
(iii)
(
2
x
2
+
2
x
+
1
)
=
0
(iv)
(
x
2
+
2
x
+
1
)
=
0
(v)
(
x
2
−
x
+
1
)
=
0
Question
14
14.
The product of the roots of the quadratic equation
(
x
2
−
12
x
+
36
)
=
0
is
(i)
37
(ii)
36
(iii)
34
(iv)
35
(v)
38
Question
15
15.
Find the discriminant of the quadratic equation
(
x
2
+
x
−
12
)
=
0
(i)
52
(ii)
48
(iii)
50
(iv)
49
(v)
46
Question
16
16.
Find the roots of the quadratic equation
(
81
x
2
+
18
x
−
3
)
=
0
(i)
(
1
3
,
-1
)
(ii)
(
1
9
,
(
-1
3
)
)
(iii)
(
1
11
,
(
-1
3
)
)
(iv)
(
1
11
,
-1
)
Question
17
17.
The sum of the roots of the quadratic equation
(
−
12
x
2
−
47
x
−
45
)
=
0
is
(i)
(
-53
14
)
(ii)
(
-41
10
)
(iii)
(
-49
12
)
(iv)
(
-47
12
)
(v)
(
-15
4
)
Question
18
18.
The sum of the roots of the quadratic equation
(
x
2
−
5
x
−
24
)
=
0
is
(i)
4
(ii)
8
(iii)
5
(iv)
6
(v)
3
Question
19
19.
The area of a rectangular room is 132.00 sq.m. If the length and breadth are increased by 6 m, the area would become 336.00 sq.m. Find the original dimensions of the room
(i)
4.00 m , 33.00 m
(ii)
2.00 m , 66.00 m
(iii)
6.00 m , 22.00 m
(iv)
3.00 m , 44.00 m
Question
20
20.
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)
24
(ii)
22
(iii)
23
(iv)
25
(v)
27
Question
21
21.
Factorize
(
x
2
+
8
x
+
15
)
(i)
(
x
+
5
)
(
x
+
3
)
(ii)
(
x
+
5
)
(
x
−
3
)
(iii)
(
x
−
5
)
(
x
+
3
)
(iv)
(
x
−
5
)
(
x
−
3
)
Question
22
22.
Solve :
(
17
x
+
1
)
(
38
x
+
1
)
=
(
32
x
+
1
)
(
71
x
+
1
)
(i)
(
-3
,
0
)
(ii)
(
3
,
4
)
(iii)
(
0
,
2
)
(iv)
(
0
,
-2
)
(v)
(
-1
,
1
)
Question
23
23.
Solve :
18
x
2
−
5
a
b
2
x
−
7
a
2
b
4
= 0
(i)
5
a
b
2
9
,
−
a
b
2
(ii)
a
b
2
,
0
(iii)
a
b
2
,
−
a
b
2
(iv)
7
a
b
2
9
,
−
a
b
2
2
(v)
7
a
b
2
11
,
−
a
b
2
3
Question
24
24.
Solve :
49
x
2
b
2
−
25
a
2
= 0
(i)
3
a
7
b
,
−
a
b
(ii)
5
a
7
b
,
−
5
a
7
b
(iii)
a
b
,
−
a
b
(iv)
5
a
9
b
,
−
5
a
9
b
(v)
a
b
,
−
3
a
7
b
Question
25
25.
Solve :
6
x
2
−
a
2
b
x
−
2
a
4
b
2
= 0
(i)
4
a
2
b
3
,
a
2
b
2
(ii)
2
a
2
b
5
,
−
a
2
b
4
(iii)
2
a
2
b
3
,
−
a
2
b
2
(iv)
2
a
2
b
,
−
a
2
b
(v)
0
,
−
3
a
2
b
2
Assignment Key
1) (i)
2) (v)
3) (iii)
4) (v)
5) (ii)
6) (ii)
7) (iv)
8) (iv)
9) (iii)
10) (iii)
11) (ii)
12) (iii)
13) (iv)
14) (ii)
15) (iv)
16) (ii)
17) (iv)
18) (iii)
19) (iii)
20) (i)
21) (i)
22) (iii)
23) (iv)
24) (ii)
25) (iii)
