EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
If
-2
is the root of
(
x
2
+
k
x
+
8
)
=
0
, find
k
and the other root
(i)
k
=
5
, and the other root =
-5
(ii)
k
=
8
, and the other root =
-1
(iii)
k
=
6
, and the other root =
-4
(iv)
k
=
4
, and the other root =
-6
(v)
k
=
7
, and the other root =
-3
Question
2
2.
Solve :
16
x
2
−
14
a
2
b
x
+
3
a
4
b
2
= 0
(i)
a
2
b
8
,
0
(ii)
3
a
2
b
8
,
2
a
2
b
4
(iii)
a
2
b
2
,
a
2
b
(iv)
3
a
2
b
10
,
a
2
b
3
(v)
5
a
2
b
8
,
a
2
b
Question
3
3.
Find the roots of the quadratic equation
(
5
x
2
+
8
x
−
3
)
=
0
(i)
(
(
−
4
5
+
1
5
4
√
31
)
,
(
−
4
5
−
1
5
√
31
)
)
(ii)
(
(
−
4
5
+
1
5
4
√
31
)
,
(
−
4
5
−
31
5
)
)
(iii)
(
(
−
4
5
+
1
5
√
31
)
,
(
−
4
5
−
1
5
√
31
)
)
(iv)
(
(
−
2
5
+
1
5
√
31
)
,
(
−
4
5
−
31
5
)
)
(v)
(
(
−
2
5
+
1
5
√
31
)
,
(
−
6
5
−
1
5
√
31
)
)
Question
4
4.
One pipe can fill a cistern in
8
hours less than the other.
The two pipes together can fill it in
6
29
30
hrs.
Find the time that each pipe will take to fill the cistern.
(i)
13 hr , 21 hr
(ii)
11 hr , 19 hr
(iii)
10 hr , 18 hr
(iv)
12 hr , 20 hr
(v)
8 hr , 16 hr
Question
5
5.
Solve :
15
x
2
−
8
√
15
x
+
12
=
0
(i)
2
√
15
,
6
√
60
(ii)
2
√
4
√
15
,
6
√
4
√
15
(iii)
2
√
60
,
6
√
60
(iv)
2
√
15
,
6
√
15
(v)
2
√
4
√
15
,
6
√
15
Question
6
6.
A two digit number is such that the product of the digits is 20. When 9 is added to the number, the digits are reversed. Find the number
(i)
45
(ii)
43
(iii)
46
(iv)
48
(v)
44
Question
7
7.
For what values of
k
are the roots of
(
k
−
56
)
x
2
+
(
k
−
41
)
x
+
(
k
+
7
)
=
0
equal
(i)
(
(
−
16
)
,
56
)
(ii)
(
(
−
19
)
,
57
)
(iii)
(
(
−
18
)
,
56
)
(iv)
(
(
−
16
)
,
54
)
(v)
(
(
−
18
)
,
57
)
Question
8
8.
39 is divided into two parts such that the sum of their reciprocals is
13
126
.
Find the two parts
(i)
(
17
,
22
)
(ii)
(
20
,
19
)
(iii)
(
19
,
20
)
(iv)
(
18
,
21
)
(v)
(
16
,
23
)
Question
9
9.
Twice the square of a number exceeds 5 times the number by 187. Find the number
(i)
11
(ii)
13
(iii)
10
(iv)
8
(v)
12
Question
10
10.
Solve :
−
42
x
2
+
√
3
x
+
3
=
0
(i)
√
12
6
,
√
3
(
−
7
)
(ii)
√
12
6
,
√
12
(
−
7
)
(iii)
√
3
6
,
√
3
(
−
7
)
(iv)
√
3
6
√
4
,
√
3
(
−
7
√
4
)
(v)
√
3
6
,
√
3
(
−
7
√
4
)
Question
11
11.
Solve :
(
2
x
+
1
)
(
x
−
1
)
+
(
x
+
2
)
(
4
x
+
1
)
=
101
26
(i)
(
(
-7
34
)
,
1
)
(ii)
(
(
-5
34
)
,
3
)
(iii)
(
(
-5
36
)
,
4
)
(iv)
(
(
-3
34
)
,
5
)
(v)
(
(
-5
32
)
,
2
)
Question
12
12.
Solve :
15
x
2
a
4
−
22
b
x
a
2
+
8
b
2
= 0
(i)
4
b
7
a
2
,
6
b
11
a
2
(ii)
4
b
5
a
2
,
6
b
9
a
2
(iii)
2
b
5
a
2
,
4
b
9
a
2
(iv)
4
b
3
a
2
,
6
b
7
a
2
(v)
6
b
5
a
2
,
8
b
9
a
2
Question
13
13.
Solve :
(
x
2
−
9
x
)
2
−
5
(
x
2
−
9
x
)
+
4
=
0
(i)
(
11
2
+
1
2
√
97
)
,
(
11
2
−
1
2
√
97
)
,
(
11
2
+
1
2
√
85
)
,
(
11
2
−
1
2
√
85
)
(ii)
(
9
2
+
1
2
√
97
)
,
(
9
2
−
1
2
√
97
)
,
(
9
2
+
1
2
√
85
)
,
(
9
2
−
1
2
√
85
)
(iii)
(
7
2
+
1
2
√
97
)
,
(
7
2
−
1
2
√
97
)
,
(
7
2
+
1
2
√
85
)
,
(
7
2
−
1
2
√
85
)
(iv)
(
9
2
+
1
2
4
√
97
)
,
(
9
2
−
1
2
4
√
97
)
,
(
9
2
+
1
2
4
√
85
)
,
(
9
2
−
1
2
4
√
85
)
(v)
(
9
2
+
97
2
)
,
(
9
2
−
97
2
)
,
(
9
2
+
85
2
)
,
(
9
2
−
85
2
)
Question
14
14.
Find the number which is less than its square by 306
(i)
16
(ii)
19
(iii)
18
(iv)
17
(v)
21
Question
15
15.
Find the roots of the quadratic equation
(
x
2
−
6
x
+
9
)
=
0
(i)
(
3
,
3
)
(ii)
(
6
,
0
)
(iii)
(
4
,
3
)
(iv)
(
4
,
2
)
(v)
(
6
,
2
)
Question
16
16.
Find the discriminant of the quadratic equation
(
25
x
2
−
5
x
)
=
0
(i)
24
(ii)
26
(iii)
25
(iv)
28
(v)
22
Question
17
17.
The sum of the squares of two consecutive even numbers is 340. Find the numbers
(i)
(-14)
,
(-12)
or
14
,
12
(ii)
(-13)
,
(-11)
or
13
,
11
(iii)
(-15)
,
(-13)
or
15
,
13
(iv)
(-11)
,
(-10)
or
11
,
10
(v)
(-16)
,
(-15)
or
16
,
15
Question
18
18.
Solve :
√
(
−
x
+
6
)
=
(
x
+
6
)
(i)
(
−
3
√
3
)
,
(
−
10
√
3
)
(ii)
(
−
3
√
4
)
,
(
−
10
√
4
)
(iii)
(
−
3
√
5
)
,
(
−
10
√
5
)
(iv)
(
−
3
)
,
(
−
10
)
(v)
(
−
3
√
2
)
,
(
−
10
√
2
)
Question
19
19.
Find the discriminant of the quadratic equation
(
4
x
2
−
8
x
+
4
)
=
0
(i)
1
(ii)
-1
(iii)
2
(iv)
-2
(v)
0
Question
20
20.
Solve :
(
x
−
8
)
(
x
−
7
)
(
x
−
6
)
(
x
−
5
)
=
120
(i)
12
,
5
(ii)
10
,
3
(iii)
11
,
4
(iv)
7
,
0
(v)
9
,
2
Question
21
21.
A can do a work in
x
days and B can do it in
(
x
+
1
)
days.
Both of them working together can do it in
9
9
37
days. Calculate
x
(i)
18
(ii)
17
(iii)
21
(iv)
19
(v)
16
Question
22
22.
Solve the quadratic equation
x
+
4
=
21
x
(i)
(
6
,
-8
)
(ii)
(
4
,
-7
)
(iii)
(
3
,
-7
)
(iv)
(
6
,
-10
)
(v)
(
4
,
-8
)
Question
23
23.
Solve :
42
x
2
+
17
b
x
−
4
b
2
= 0
(i)
b
2
,
−
2
b
7
(ii)
−
b
6
,
−
6
b
7
(iii)
b
6
,
−
4
b
7
(iv)
b
8
,
−
4
b
9
(v)
b
4
,
−
4
b
5
Question
24
24.
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)
24
(iii)
25
(iv)
26
(v)
23
Question
25
25.
Solve :
15
x
2
a
4
b
2
−
7
x
a
2
b
−
4
= 0
(i)
2
5
a
2
b
,
−
1
a
2
b
(ii)
4
7
a
2
b
,
−
1
5
a
2
b
(iii)
4
3
a
2
b
,
−
1
a
2
b
(iv)
4
5
a
2
b
,
−
1
3
a
2
b
(v)
6
5
a
2
b
,
1
3
a
2
b
Assignment Key
1) (iii)
2) (ii)
3) (iii)
4) (ii)
5) (iv)
6) (i)
7) (ii)
8) (iv)
9) (i)
10) (iii)
11) (ii)
12) (ii)
13) (ii)
14) (iii)
15) (i)
16) (iii)
17) (i)
18) (iv)
19) (v)
20) (ii)
21) (i)
22) (iii)
23) (iii)
24) (ii)
25) (iv)
