EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
The sum of the roots of the quadratic equation
(
x
2
+
3
x
−
54
)
=
0
is
(i)
0
(ii)
-2
(iii)
-5
(iv)
-3
(v)
-4
Question
2
2.
Find the discriminant of the quadratic equation
(
x
2
+
2
x
+
1
)
=
0
(i)
3
(ii)
-2
(iii)
-1
(iv)
1
(v)
0
Question
3
3.
Find the roots of the quadratic equation
(
18
x
2
−
15
x
+
2
)
=
0
(i)
(
4
3
,
1
4
)
(ii)
(
4
3
,
(
-1
6
)
)
(iii)
(
2
5
,
1
6
)
(iv)
(
2
3
,
1
6
)
(v)
(
2
5
,
1
4
)
Question
4
4.
Find the quadratic equation with roots
(
(
-9
2
)
,
1
5
)
(i)
(
14
x
2
+
61
x
−
9
)
=
0
(ii)
(
10
x
2
+
43
x
−
9
)
=
0
(iii)
(
10
x
2
+
39
x
−
27
)
=
0
(iv)
(
5
x
2
+
44
x
−
9
)
=
0
(v)
(
10
x
2
+
53
x
−
11
)
=
0
Question
5
5.
Find the roots of the quadratic equation correct to two decimal places
(
−
36
x
2
+
11
x
+
12
)
=
0
(i)
7.56 , 8.75
(ii)
0.56 , 1.75
(iii)
-0.44 , 0.75
(iv)
6.56 , 7.75
(v)
1.56 , 2.75
Question
6
6.
Solve :
8
x
2
+
2
a
b
2
x
−
a
2
b
4
= 0
(i)
−
a
b
2
4
,
−
3
a
b
2
2
(ii)
a
b
2
4
,
−
a
b
2
2
(iii)
a
b
2
6
,
−
a
b
2
4
(iv)
a
b
2
2
,
−
a
b
2
(v)
3
a
b
2
4
,
a
b
2
2
Question
7
7.
Solve :
8
x
2
b
2
−
10
a
2
x
b
+
3
a
4
= 0
(i)
a
2
b
,
3
a
2
2
b
(ii)
a
2
2
b
,
3
a
2
4
b
(iii)
a
2
4
b
,
a
2
2
b
(iv)
−
a
2
2
b
,
a
2
4
b
(v)
3
a
2
2
b
,
5
a
2
4
b
Question
8
8.
Solve :
(
x
(
x
−
5
)
)
2
+
11
(
x
(
x
−
5
)
)
+
18
= 0
(i)
4
,
11
2
(ii)
8
3
,
7
2
(iii)
10
3
,
9
2
(iv)
16
5
,
17
4
(v)
4
,
5
Question
9
9.
One pipe can fill a cistern in
5
hours less than the other.
The two pipes together can fill it in
8
2
33
hrs.
Find the time that each pipe will take to fill the cistern.
(i)
12 hr , 16 hr
(ii)
14 hr , 19 hr
(iii)
15 hr , 20 hr
(iv)
13 hr , 18 hr
(v)
16 hr , 21 hr
Question
10
10.
Solve :
x
2
+
10
x
+
14
=
0
(i)
(
−
5
√
4
+
√
11
)
,
(
−
5
√
4
−
√
11
)
(ii)
(
−
5
+
√
33
)
,
(
−
5
−
√
33
)
(iii)
(
−
5
√
5
+
√
11
)
,
(
−
5
√
5
−
√
11
)
(iv)
(
−
5
+
√
11
)
,
(
−
5
−
√
11
)
(v)
(
−
5
+
√
22
)
,
(
−
5
−
√
22
)
Question
11
11.
Solve :
12
x
2
+
26
√
3
x
+
36
=
0
(i)
(
−
9
√
4
)
√
12
,
(
−
4
)
√
12
(ii)
(
−
9
)
√
12
,
(
−
4
)
√
12
(iii)
(
−
9
)
√
48
,
(
−
4
)
√
48
(iv)
(
−
9
√
4
)
√
12
,
(
−
4
√
4
)
√
12
(v)
(
−
9
)
√
12
,
(
−
4
)
√
48
Question
12
12.
Find the quadratic equation with roots
(
(
-7
2
)
,
(
-7
2
)
)
(i)
(
4
x
2
+
28
x
+
49
)
=
0
(ii)
(
2
x
2
+
21
x
+
49
)
=
0
(iii)
(
4
x
2
+
32
x
+
63
)
=
0
(iv)
(
4
x
2
+
24
x
+
35
)
=
0
(v)
(
8
x
2
+
42
x
+
49
)
=
0
Question
13
13.
A stream flows from A to B, a distance of 9.00 km. A man who can row in still water at 6.00 kmph, can row up and down in 4.00 hr . What is the speed of the stream?
(i)
3.00 kmph
(ii)
2.00 kmph
(iii)
1.00 kmph
(iv)
4.00 kmph
(v)
5.00 kmph
Question
14
14.
Solve :
18
x
2
a
−
12
x
+
3
x
a
−
2
= 0
(i)
4
6
a
,
−
1
6
(ii)
1
2
a
,
−
1
8
(iii)
1
3
a
,
−
1
2
(iv)
1
a
,
1
6
(v)
1
a
,
−
1
4
Question
15
15.
Find the roots of the quadratic equation
(
x
2
−
11
x
+
30
)
=
0
(i)
(
8
,
2
)
(ii)
(
6
,
5
)
(iii)
(
7
,
5
)
(iv)
(
8
,
4
)
(v)
(
7
,
4
)
Question
16
16.
For what values of
k
are the roots of
(
k
−
10
)
x
2
+
(
k
+
45
)
x
+
(
k
+
29
)
=
0
equal
(i)
(
(
−
91
3
)
,
35
)
(ii)
(
(
−
89
3
)
,
33
)
(iii)
(
(
−
89
3
)
,
34
)
(iv)
(
(
−
151
5
)
,
35
)
(v)
(
(
−
151
5
)
,
34
)
Question
17
17.
Find the number which exceeds its reciprocal by
17
17
18
(i)
17
(ii)
18
(iii)
20
(iv)
19
(v)
15
Question
18
18.
Find the quadratic equation, the sum of whose roots is
16
and product is
64
(i)
(
x
2
−
13
x
+
64
)
=
0
(ii)
(
−
16
x
+
64
)
=
0
(iii)
(
x
2
−
16
x
+
64
)
=
0
(iv)
(
x
2
−
19
x
+
64
)
=
0
(v)
(
2
x
2
−
16
x
+
64
)
=
0
Question
19
19.
The perimeter of a rectangular room is 50.00 m and the length of its diagonal is 19.31 m . Find the dimensions of the room
(i)
20.00 m , 5.00 m
(ii)
18.00 m , 7.00 m
(iii)
19.00 m , 6.00 m
(iv)
16.00 m , 9.00 m
(v)
17.00 m , 8.00 m
Question
20
20.
A play field is
70.00 m
by
50.00 m
.
It has a road all around it on the outside.
Find the width of the road if its area is
29
28
of the area of the play field
(i)
13.50 m
(ii)
14.50 m
(iii)
12.50 m
(iv)
10.50 m
(v)
11.50 m
Question
21
21.
The sum of the numerator and denominator of a fraction is
36
.
If
5
is added to both the numerator and denominator,
the fraction is increased by
20
297
. Find the fraction
(i)
7
10
(ii)
8
11
(iii)
22
14
(iv)
6
11
(v)
14
22
Question
22
22.
Solve :
−
24
x
2
+
2
√
3
x
+
3
=
0
(i)
√
12
4
,
√
3
(
−
6
)
(ii)
√
3
4
√
4
,
√
3
(
−
6
√
4
)
(iii)
√
3
4
,
√
3
(
−
6
√
4
)
(iv)
√
12
4
,
√
12
(
−
6
)
(v)
√
3
4
,
√
3
(
−
6
)
Question
23
23.
Solve :
4
x
2
+
2
x
−
2
x
b
−
b
= 0
(i)
−
1
2
,
b
2
(ii)
−
1
,
b
(iii)
−
3
2
,
−
b
2
(iv)
−
1
4
,
b
4
(v)
1
2
,
3
b
2
Question
24
24.
If
p
and
q
are the roots of
(
x
2
+
x
−
42
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
42
x
2
+
29
x
−
1763
)
=
0
(ii)
(
28
x
2
+
39
x
−
1189
)
=
0
(iii)
(
42
x
2
+
41
x
−
1681
)
=
0
(iv)
(
18
x
2
+
21
x
−
697
)
=
0
(v)
(
42
x
2
+
55
x
−
1763
)
=
0
Question
25
25.
Find the quadratic equation with roots
(
3
,
-1
)
(i)
(
x
2
−
3
x
)
=
0
(ii)
(
x
2
−
4
x
+
3
)
=
0
(iii)
(
x
2
−
x
−
2
)
=
0
(iv)
(
x
2
−
2
x
−
3
)
=
0
(v)
(
x
2
−
1
)
=
0
Assignment Key
1) (iv)
2) (v)
3) (iv)
4) (ii)
5) (iii)
6) (ii)
7) (ii)
8) (iii)
9) (ii)
10) (iv)
11) (ii)
12) (i)
13) (i)
14) (i)
15) (ii)
16) (i)
17) (ii)
18) (iii)
19) (ii)
20) (iii)
21) (v)
22) (v)
23) (i)
24) (iii)
25) (iv)
