EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Solve :
14
x
2
+
17
a
2
b
x
+
5
a
4
b
2
= 0
(i)
−
a
2
b
,
−
3
a
2
b
2
(ii)
−
a
2
b
,
−
a
2
b
(iii)
−
5
a
2
b
7
,
−
a
2
b
2
(iv)
−
3
a
2
b
7
,
a
2
b
2
(v)
−
5
a
2
b
9
,
−
a
2
b
4
Question
2
2.
Solve :
(
x
(
x
−
1
)
)
2
+
15
(
x
(
x
−
1
)
)
+
54
= 0
(i)
6
5
,
9
8
(ii)
4
7
,
7
10
(iii)
8
7
,
11
10
(iv)
2
3
,
3
4
(v)
6
7
,
9
10
Question
3
3.
Find the discriminant of the quadratic equation
(
−
2
x
2
−
9
x
−
17
)
=
0
(i)
-55
(ii)
-57
(iii)
-54
(iv)
-56
(v)
-52
Question
4
4.
The sum of the squares of two consecutive odd numbers is 74. Find the numbers
(i)
(-7)
,
(-5)
or
7
,
5
(ii)
(-5)
,
(-2)
or
5
,
2
(iii)
(-9)
,
(-8)
or
9
,
8
(iv)
(-6)
,
(-4)
or
6
,
4
(v)
(-8)
,
(-6)
or
8
,
6
Question
5
5.
Find the discriminant of the quadratic equation
(
x
2
−
4
)
=
0
(i)
15
(ii)
18
(iii)
16
(iv)
14
(v)
17
Question
6
6.
Find the number which exceeds its reciprocal by
5
5
6
(i)
8
(ii)
7
(iii)
5
(iv)
6
(v)
3
Question
7
7.
If
-4
is the root of
(
x
2
+
k
x
+
20
)
=
0
, find
k
and the other root
(i)
k
=
10
, and the other root =
-4
(ii)
k
=
8
, and the other root =
-6
(iii)
k
=
9
, and the other root =
-5
(iv)
k
=
6
, and the other root =
-8
(v)
k
=
11
, and the other root =
-3
Question
8
8.
44 is divided into two parts such that the sum of their reciprocals is
4
33
.
Find the two parts
(i)
(
13
,
31
)
(ii)
(
12
,
32
)
(iii)
(
11
,
33
)
(iv)
(
9
,
35
)
(v)
(
10
,
34
)
Question
9
9.
In a two digit number, the unit's digit exceeds it ten's digit by 3 and the product of the given number and the sum of its digits is equal to 754 . Find the number
(i)
58
(ii)
36
(iii)
69
(iv)
80
(v)
47
Question
10
10.
A play field is
90.00 m
by
80.00 m
.
It has a road all around it on the outside.
Find the width of the road if its area is
25
9
of the area of the play field
(i)
38.00 m
(ii)
40.00 m
(iii)
42.00 m
(iv)
39.00 m
(v)
41.00 m
Question
11
11.
Find the discriminant of the quadratic equation
(
x
2
−
x
+
3
)
=
0
(i)
-14
(ii)
-10
(iii)
-11
(iv)
-9
(v)
-12
Question
12
12.
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)
22
(ii)
25
(iii)
24
(iv)
26
(v)
23
Question
13
13.
The sum of the squares of two consecutive even numbers is 164. Find the numbers
(i)
5
,
8
or
(-5)
,
(-8)
(ii)
8
,
10
or
(-8)
,
(-10)
(iii)
7
,
9
or
(-7)
,
(-9)
(iv)
11
,
13
or
(-11)
,
(-13)
(v)
9
,
11
or
(-9)
,
(-11)
Question
14
14.
Solve :
(
x
−
2
)
(
x
−
1
)
x
(
x
+
1
)
=
840
(i)
5
,
(
−
6
)
(ii)
6
,
(
−
5
)
(iii)
7
,
(
−
4
)
(iv)
4
,
(
−
8
)
(v)
9
,
(
−
3
)
Question
15
15.
Solve :
√
(
4
x
2
+
25
x
+
25
)
=
(
x
−
7
)
(i)
(
−
13
2
−
1
2
√
402
)
,
(
−
13
2
+
1
2
√
402
)
(ii)
(
−
13
2
√
4
−
1
2
√
201
)
,
(
−
13
2
√
4
+
1
2
√
201
)
(iii)
(
−
13
2
−
1
2
√
201
)
,
(
−
13
2
+
1
2
√
201
)
(iv)
(
−
13
2
−
1
2
√
603
)
,
(
−
13
2
+
1
2
√
603
)
(v)
(
−
13
2
√
5
−
1
2
√
201
)
,
(
−
13
2
√
5
+
1
2
√
201
)
Question
16
16.
Solve :
4
√
11
x
2
+
21
x
−
8
√
11
=
0
(i)
√
44
4
,
(
−
8
√
4
)
√
11
(ii)
√
44
4
,
(
−
8
)
√
11
(iii)
√
11
4
,
(
−
8
)
√
44
(iv)
√
11
4
,
(
−
8
)
√
11
(v)
√
11
4
√
4
,
(
−
8
)
√
44
Question
17
17.
Find the roots of the quadratic equation correct to two decimal places
(
10
x
2
−
13
x
−
3
)
=
0
(i)
0.50 , 6.80
(ii)
2.50 , 0.80
(iii)
1.50 , -0.20
(iv)
3.50 , 1.80
(v)
9.50 , 7.80
Question
18
18.
If the difference of two numbers is 3 and their product is 180, find the numbers
(i)
(-13)
,
(-16)
or
13
,
16
(ii)
(-15)
,
(-18)
or
15
,
18
(iii)
(-12)
,
(-15)
or
12
,
15
(iv)
(-11)
,
(-14)
or
11
,
14
(v)
(-9)
,
(-13)
or
9
,
13
Question
19
19.
Solve :
12
x
2
+
13
a
x
+
3
a
2
= 0
(i)
−
a
2
,
−
a
9
(ii)
−
3
a
5
,
−
3
a
11
(iii)
−
a
,
−
3
a
7
(iv)
−
3
a
4
,
−
a
3
(v)
−
a
,
−
5
a
9
Question
20
20.
For what values of
k
are the roots of
(
k
+
17
)
x
2
+
(
k
+
10
)
x
+
(
k
−
23
)
=
0
equal
(i)
(
(
−
50
3
)
,
30
)
(ii)
(
(
−
86
5
)
,
31
)
(iii)
(
(
−
50
3
)
,
31
)
(iv)
(
(
−
86
5
)
,
32
)
(v)
(
(
−
52
3
)
,
32
)
Question
21
21.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 77 . Find the three numbers.
(i)
11, 12, 13
(ii)
8, 9, 10
(iii)
10, 11, 12
(iv)
9, 10, 11
(v)
13, 14, 15
Question
22
22.
The area of a rectangular room is 88.00 sq.m. If the length and breadth are increased by 4 m, the area would become 288.00 sq.m. Find the original dimensions of the room
(i)
44.00 m , 2.00 m
(ii)
4.00 m , 22.00 m
(iii)
7.00 m , 12.57 m
(iv)
3.00 m , 29.33 m
(v)
8.00 m , 11.00 m
Question
23
23.
Solve :
−
5
(
x
+
5
)
−
1
(
−
x
−
4
)
=
−
5
(i)
(
−
5
√
3
)
,
(
−
4
√
3
)
(ii)
(
−
5
√
2
)
,
(
−
4
√
2
)
(iii)
(
−
5
√
5
)
,
(
−
4
√
5
)
(iv)
(
−
5
√
4
)
,
(
−
4
√
4
)
(v)
(
−
5
)
,
(
−
4
)
Question
24
24.
Solve :
27
x
2
a
2
−
21
x
a
+
4
= 0
(i)
2
3
a
,
1
a
(ii)
4
9
a
,
1
3
a
(iii)
4
7
a
,
1
a
(iv)
4
11
a
,
1
5
a
(v)
2
9
a
,
−
1
3
a
Question
25
25.
A two digit number is such that the product of the digits is 5. When 36 is subtracted from the number, the digits are reversed. Find the number
(i)
52
(ii)
51
(iii)
48
(iv)
54
(v)
50
Assignment Key
1) (iii)
2) (v)
3) (i)
4) (i)
5) (iii)
6) (iv)
7) (iii)
8) (iii)
9) (i)
10) (ii)
11) (iii)
12) (iii)
13) (ii)
14) (ii)
15) (iii)
16) (iv)
17) (iii)
18) (iii)
19) (iv)
20) (v)
21) (iii)
22) (i)
23) (v)
24) (ii)
25) (ii)
