EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
A stream flows from A to B, a distance of 12.00 km. A man who can row in still water at 9.00 kmph, can row up and down in 2.81 hr . What is the speed of the stream?
(i)
0.00 kmph
(ii)
4.00 kmph
(iii)
2.00 kmph
(iv)
3.00 kmph
(v)
1.00 kmph
Question
2
2.
59 is divided into two parts such that the sum of their reciprocals is
59
814
.
Find the two parts
(i)
(
35
,
24
)
(ii)
(
37
,
22
)
(iii)
(
39
,
20
)
(iv)
(
36
,
23
)
(v)
(
38
,
21
)
Question
3
3.
Solve :
35
x
2
b
2
+
44
a
2
x
b
+
12
a
4
= 0
(i)
−
4
a
2
7
b
,
0
(ii)
−
6
a
2
7
b
,
−
2
a
2
5
b
(iii)
−
8
a
2
7
b
,
−
4
a
2
5
b
(iv)
−
2
a
2
3
b
,
−
2
a
2
7
b
(v)
−
6
a
2
5
b
,
−
2
a
2
3
b
Question
4
4.
Solve :
√
(
2
x
2
+
15
x
−
8
)
=
(
x
−
6
)
(i)
(
−
27
2
√
4
−
1
2
√
905
)
,
(
−
27
2
√
4
+
1
2
√
905
)
(ii)
(
−
27
2
−
1
2
√
1810
)
,
(
−
27
2
+
1
2
√
1810
)
(iii)
(
−
27
2
−
1
2
√
905
)
,
(
−
27
2
+
1
2
√
905
)
(iv)
(
−
27
2
√
5
−
1
2
√
905
)
,
(
−
27
2
√
5
+
1
2
√
905
)
(v)
(
−
27
2
−
1
2
√
2715
)
,
(
−
27
2
+
1
2
√
2715
)
Question
5
5.
Solve :
4
√
7
x
2
+
17
x
−
6
√
7
=
0
(i)
√
7
4
,
(
−
6
)
√
28
(ii)
√
7
4
,
(
−
6
)
√
7
(iii)
√
28
4
,
(
−
6
√
4
)
√
7
(iv)
√
7
4
√
4
,
(
−
6
)
√
28
(v)
√
28
4
,
(
−
6
)
√
7
Question
6
6.
Find the discriminant of the quadratic equation
(
−
6
x
2
+
9
x
−
3
)
=
0
(i)
8
(ii)
6
(iii)
9
(iv)
11
(v)
10
Question
7
7.
Solve :
−
5
(
x
−
5
)
−
3
(
x
−
1
)
=
−
3
(i)
5
√
2
,
√
2
(ii)
5
√
3
,
√
3
(iii)
5
,
1
(iv)
5
√
4
,
√
4
(v)
5
√
5
,
√
5
Question
8
8.
The sum of the squares of two consecutive even numbers is 164. Find the numbers
(i)
7
,
9
or
(-7)
,
(-9)
(ii)
10
,
13
or
(-10)
,
(-13)
(iii)
6
,
8
or
(-6)
,
(-8)
(iv)
9
,
11
or
(-9)
,
(-11)
(v)
8
,
10
or
(-8)
,
(-10)
Question
9
9.
Solve :
(
x
−
9
)
(
x
−
4
)
+
(
x
+
2
)
(
x
−
6
)
=
101
35
(i)
(
70
29
,
10
)
(ii)
(
76
31
,
14
)
(iii)
(
74
31
,
11
)
(iv)
(
26
11
,
12
)
(v)
(
72
31
,
8
)
Question
10
10.
A can do a work in
x
days and B can do it in
(
x
+
8
)
days.
Both of them working together can do it in
13
5
7
days. Calculate
x
(i)
21
(ii)
25
(iii)
23
(iv)
27
(v)
24
Question
11
11.
Find the roots of the quadratic equation
(
x
2
−
2
x
+
1
)
=
0
(i)
(
3
,
-1
)
(ii)
(
3
,
0
)
(iii)
(
2
,
0
)
(iv)
(
2
,
1
)
(v)
(
1
,
1
)
Question
12
12.
Solve :
(
x
2
−
x
)
2
−
4
(
x
2
−
x
)
+
3
=
0
(i)
(
1
2
+
1
2
√
13
)
,
(
1
2
−
1
2
√
13
)
,
(
1
2
+
1
2
√
5
)
,
(
1
2
−
1
2
√
5
)
(ii)
(
−
1
2
+
1
2
√
13
)
,
(
−
1
2
−
1
2
√
13
)
,
(
−
1
2
+
1
2
√
5
)
,
(
−
1
2
−
1
2
√
5
)
(iii)
(
3
2
+
1
2
√
13
)
,
(
3
2
−
1
2
√
13
)
,
(
3
2
+
1
2
√
5
)
,
(
3
2
−
1
2
√
5
)
(iv)
(
1
2
+
13
2
)
,
(
1
2
−
13
2
)
,
(
1
2
+
5
2
)
,
(
1
2
−
5
2
)
(v)
(
1
2
+
1
2
4
√
13
)
,
(
1
2
−
1
2
4
√
13
)
,
(
1
2
+
1
2
4
√
5
)
,
(
1
2
−
1
2
4
√
5
)
Question
13
13.
Find the roots of the quadratic equation
(
8
x
2
+
12
x
−
20
)
=
0
(i)
(
4
,
(
-7
2
)
)
(ii)
(
2
,
-3
)
(iii)
(
1
,
(
-5
2
)
)
(iv)
(
4
,
-3
)
(v)
(
2
,
(
-5
2
)
)
Question
14
14.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 12 . Find the three numbers.
(i)
5, 6, 7
(ii)
6, 7, 8
(iii)
4, 5, 6
(iv)
8, 9, 10
(v)
2, 3, 4
Question
15
15.
Solve the quadratic equation
x
+
7
=
−
6
x
(i)
(
1
,
-9
)
(ii)
(
0
,
-6
)
(iii)
(
-1
,
-6
)
(iv)
(
0
,
-7
)
(v)
(
1
,
-7
)
Question
16
16.
The area of a rectangular room is 300.00 sq.m. If the length and breadth are increased by 10 m, the area would become 1430.00 sq.m. Find the original dimensions of the room
(i)
4.00 m , 75.00 m
(ii)
3.00 m , 100.00 m
(iii)
5.00 m , 60.00 m
Question
17
17.
Solve :
36
x
2
+
5
a
2
b
x
−
a
4
b
2
= 0
(i)
−
a
2
b
4
,
a
2
b
9
(ii)
−
a
2
b
6
,
a
2
b
11
(iii)
−
a
2
b
2
,
a
2
b
7
(iv)
a
2
b
4
,
a
2
b
3
(v)
−
3
a
2
b
4
,
−
a
2
b
9
Question
18
18.
One pipe can fill a cistern in
2
hours less than the other.
The two pipes together can fill it in
4
19
20
hrs.
Find the time that each pipe will take to fill the cistern.
(i)
9 hr , 11 hr
(ii)
10 hr , 12 hr
(iii)
12 hr , 14 hr
(iv)
8 hr , 10 hr
(v)
6 hr , 9 hr
Question
19
19.
If the difference of two numbers is 8 and their product is 240, find the numbers
(i)
23
,
14
or
(-23)
,
(-14)
(ii)
17
,
10
or
(-17)
,
(-10)
(iii)
20
,
12
or
(-20)
,
(-12)
(iv)
19
,
11
or
(-19)
,
(-11)
(v)
21
,
13
or
(-21)
,
(-13)
Question
20
20.
For what values of
k
are the roots of
(
k
−
8
)
x
2
+
(
k
+
8
)
x
+
(
k
−
8
)
=
0
equal
(i)
(
12
5
,
24
)
(ii)
(
10
3
,
23
)
(iii)
(
10
3
,
22
)
(iv)
(
8
3
,
24
)
(v)
(
12
5
,
23
)
Question
21
21.
Find two natural numbers which differ by 18 and the sum of whose squares is 362
(i)
(
4
,
22
)
(ii)
(
0
,
18
)
(iii)
(
-1
,
16
)
(iv)
(
2
,
20
)
(v)
(
1
,
19
)
Question
22
22.
Solve :
32
x
2
a
2
+
36
x
a
+
9
= 0
(i)
−
3
2
a
,
−
1
2
a
(ii)
−
1
2
a
,
−
3
10
a
(iii)
−
1
4
a
,
−
1
8
a
(iv)
−
5
4
a
,
−
5
8
a
(v)
−
3
4
a
,
−
3
8
a
Question
23
23.
Find the discriminant of the quadratic equation
(
x
2
−
10
x
+
25
)
=
0
(i)
-1
(ii)
1
(iii)
0
(iv)
-3
(v)
2
Question
24
24.
Solve :
15
x
2
−
2
√
15
x
−
48
=
0
(i)
8
√
60
,
(
−
6
)
√
60
(ii)
8
√
15
,
(
−
6
)
√
15
(iii)
8
√
15
,
(
−
6
)
√
60
(iv)
8
√
4
√
15
,
(
−
6
√
4
)
√
15
(v)
8
√
4
√
15
,
(
−
6
)
√
15
Question
25
25.
Solve :
24
x
2
b
2
−
29
a
x
b
+
7
a
2
= 0
(i)
5
a
8
b
,
−
a
3
b
(ii)
7
a
8
b
,
a
3
b
(iii)
7
a
6
b
,
a
b
(iv)
7
a
10
b
,
a
5
b
(v)
9
a
8
b
,
a
b
Assignment Key
1) (iii)
2) (ii)
3) (ii)
4) (iii)
5) (ii)
6) (iii)
7) (iii)
8) (v)
9) (iii)
10) (v)
11) (v)
12) (i)
13) (iii)
14) (i)
15) (iii)
16) (ii)
17) (i)
18) (i)
19) (iii)
20) (iv)
21) (v)
22) (v)
23) (iii)
24) (ii)
25) (ii)
