EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Solve :
10
x
2
+
5
√
10
x
−
6
=
0
(i)
√
4
√
10
,
(
−
6
)
√
10
(ii)
1
√
10
,
(
−
6
)
√
10
(iii)
1
√
10
,
(
−
6
)
√
40
(iv)
1
√
40
,
(
−
6
)
√
40
(v)
√
4
√
10
,
(
−
6
√
4
)
√
10
Question
2
2.
Find the discriminant of the quadratic equation
(
x
2
−
8
x
+
16
)
=
0
(i)
0
(ii)
3
(iii)
1
(iv)
-1
(v)
-3
Question
3
3.
Find the number which exceeds its reciprocal by
7
7
8
(i)
8
(ii)
7
(iii)
5
(iv)
11
(v)
9
Question
4
4.
Solve :
18
x
2
+
19
a
2
b
x
+
5
a
4
b
2
= 0
(i)
−
5
a
2
b
9
,
−
a
2
b
2
(ii)
−
a
2
b
3
,
−
a
2
b
4
(iii)
−
5
a
2
b
11
,
−
2
a
2
b
5
(iv)
−
5
a
2
b
7
,
−
2
a
2
b
3
(v)
−
7
a
2
b
9
,
−
3
a
2
b
4
Question
5
5.
Solve :
−
3
(
x
−
4
)
−
4
(
−
x
−
2
)
=
3
(
x
+
1
)
(i)
(
−
15
4
+
1
4
√
241
)
,
(
−
15
4
−
1
4
√
241
)
(ii)
(
−
15
4
+
1
4
√
723
)
,
(
−
15
4
−
1
4
√
723
)
(iii)
(
−
15
4
√
4
+
1
4
√
241
)
,
(
−
15
4
√
4
−
1
4
√
241
)
(iv)
(
−
15
4
√
5
+
1
4
√
241
)
,
(
−
15
4
√
5
−
1
4
√
241
)
(v)
(
−
15
4
+
1
4
√
482
)
,
(
−
15
4
−
1
4
√
482
)
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
+
1
4
√
21
)
)
(ii)
(
(
5
4
−
1
4
√
21
)
,
(
3
4
+
21
4
)
)
(iii)
(
(
5
4
−
1
4
√
21
)
,
(
1
4
+
1
4
√
21
)
)
(iv)
(
(
3
4
−
1
4
4
√
21
)
,
(
3
4
+
21
4
)
)
(v)
(
(
3
4
−
1
4
√
21
)
,
(
3
4
+
1
4
√
21
)
)
Question
7
7.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60 . Find the three numbers.
(i)
10, 11, 12
(ii)
8, 9, 10
(iii)
9, 10, 11
(iv)
11, 12, 13
(v)
6, 7, 8
Question
8
8.
Solve :
−
42
x
2
+
√
6
x
+
6
=
0
(i)
√
6
6
√
4
,
√
6
(
−
7
√
4
)
(ii)
√
24
6
,
√
6
(
−
7
)
(iii)
√
6
6
,
√
6
(
−
7
)
(iv)
√
6
6
,
√
6
(
−
7
√
4
)
(v)
√
24
6
,
√
24
(
−
7
)
Question
9
9.
Solve :
x
2
−
4
x
−
8
=
0
(i)
(
2
√
4
+
√
12
)
,
(
2
√
4
−
√
12
)
(ii)
(
2
+
√
12
)
,
(
2
−
√
12
)
(iii)
(
2
√
5
+
√
12
)
,
(
2
√
5
−
√
12
)
(iv)
(
2
+
√
24
)
,
(
2
−
√
24
)
(v)
(
2
+
√
36
)
,
(
2
−
√
36
)
Question
10
10.
Solve :
48
x
2
a
4
+
14
b
x
a
2
+
b
2
= 0
(i)
−
b
2
a
2
,
−
3
b
8
a
2
(ii)
b
6
a
2
,
b
8
a
2
(iii)
−
b
8
a
2
,
−
b
10
a
2
(iv)
−
b
4
a
2
,
−
b
6
a
2
(v)
−
b
6
a
2
,
−
b
8
a
2
Question
11
11.
The sum of the numerator and denominator of a fraction is
35
.
If
5
is added to both the numerator and denominator,
the fraction is increased by
85
806
. Find the fraction
(i)
26
9
(ii)
7
26
(iii)
3
8
(iv)
9
26
(v)
11
26
Question
12
12.
A stream flows from A to B, a distance of 13.00 km. A man who can row in still water at 5.00 kmph, can row up and down in 14.44 hr . What is the speed of the stream?
(i)
2.00 kmph
(ii)
6.00 kmph
(iii)
4.00 kmph
(iv)
3.00 kmph
(v)
5.00 kmph
Question
13
13.
Solve :
42
x
2
+
5
b
x
−
25
b
2
= 0
(i)
5
b
9
,
−
5
b
8
(ii)
b
,
−
b
2
(iii)
3
b
7
,
−
7
b
6
(iv)
b
,
−
5
b
4
(v)
5
b
7
,
−
5
b
6
Question
14
14.
The sum of the squares of two consecutive odd numbers is 650. Find the numbers
(i)
(-22)
,
(-20)
or
22
,
20
(ii)
(-18)
,
(-16)
or
18
,
16
(iii)
(-20)
,
(-18)
or
20
,
18
(iv)
(-19)
,
(-17)
or
19
,
17
(v)
(-17)
,
(-14)
or
17
,
14
Question
15
15.
The perimeter of a rectangular room is 64.00 m and the length of its diagonal is 31.02 m . Find the dimensions of the room
(i)
23.00 m , 9.00 m
(ii)
29.00 m , 3.00 m
(iii)
30.00 m , 2.00 m
(iv)
32.00 m , 0.00 m
(v)
31.00 m , 1.00 m
Question
16
16.
Find the discriminant of the quadratic equation
(
x
2
+
5
)
=
0
(i)
-18
(ii)
-19
(iii)
-22
(iv)
-20
(v)
-21
Question
17
17.
Solve :
8
x
2
b
2
−
2
a
x
b
−
3
a
2
= 0
(i)
3
a
4
b
,
−
a
2
b
(ii)
3
a
2
b
,
−
a
b
(iii)
5
a
4
b
,
0
(iv)
a
2
b
,
−
a
3
b
(v)
a
4
b
,
−
a
b
Question
18
18.
Find the roots of the quadratic equation correct to two decimal places
(
24
x
2
+
2
x
−
1
)
=
0
(i)
1.17 , 0.75
(ii)
8.17 , 7.75
(iii)
0.17 , -0.25
(iv)
7.17 , 6.75
(v)
2.17 , 1.75
Question
19
19.
Solve :
(
x
−
8
)
(
x
−
11
)
+
(
x
−
6
)
(
x
−
10
)
=
29
6
(i)
(
176
17
,
11
)
(ii)
(
180
17
,
15
)
(iii)
(
158
15
,
12
)
(iv)
(
178
17
,
13
)
(v)
(
198
19
,
14
)
Question
20
20.
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 238 . Find the number
(i)
56
(ii)
23
(iii)
12
(iv)
45
(v)
34
Question
21
21.
If
-3
is the root of
(
x
2
+
k
x
+
21
)
=
0
, find
k
and the other root
(i)
k
=
13
, and the other root =
-5
(ii)
k
=
9
, and the other root =
-8
(iii)
k
=
10
, and the other root =
-7
(iv)
k
=
11
, and the other root =
-6
(v)
k
=
7
, and the other root =
-10
Question
22
22.
One pipe can fill a cistern in
9
hours less than the other.
The two pipes together can fill it in
8
6
35
hrs.
Find the time that each pipe will take to fill the cistern.
(i)
14 hr , 23 hr
(ii)
16 hr , 25 hr
(iii)
12 hr , 21 hr
(iv)
13 hr , 22 hr
(v)
10 hr , 20 hr
Question
23
23.
71 is divided into two parts such that the sum of their reciprocals is
71
1188
.
Find the two parts
(i)
(
45
,
26
)
(ii)
(
43
,
28
)
(iii)
(
46
,
25
)
(iv)
(
42
,
29
)
(v)
(
44
,
27
)
Question
24
24.
A play field is
50.00 m
by
30.00 m
.
It has a road all around it on the outside.
Find the width of the road if its area is
11
5
of the area of the play field
(i)
13.00 m
(ii)
14.00 m
(iii)
16.00 m
(iv)
17.00 m
(v)
15.00 m
Question
25
25.
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)
25
(iii)
26
(iv)
21
(v)
23
Assignment Key
1) (ii)
2) (i)
3) (i)
4) (i)
5) (i)
6) (v)
7) (iii)
8) (iii)
9) (ii)
10) (v)
11) (iv)
12) (iii)
13) (v)
14) (iv)
15) (v)
16) (iv)
17) (i)
18) (iii)
19) (iv)
20) (v)
21) (iii)
22) (iv)
23) (v)
24) (v)
25) (i)
