EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
A can do a work in
x
days and B can do it in
(
x
−
7
)
days.
Both of them working together can do it in
8
2
5
days. Calculate
x
(i)
23
(ii)
20
(iii)
21
(iv)
18
(v)
22
Question
2
2.
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 405 . Find the number
(i)
56
(ii)
45
(iii)
34
(iv)
67
(v)
23
Question
3
3.
Solve :
18
x
2
−
7
a
x
−
a
2
= 0
(i)
0
,
−
a
3
(ii)
a
,
a
9
(iii)
a
,
−
a
7
(iv)
a
3
,
−
a
11
(v)
2
a
4
,
−
a
9
Question
4
4.
Solve :
6
x
2
a
2
+
x
a
−
2
= 0
(i)
−
2
3
a
,
3
6
a
(ii)
−
2
a
,
3
4
a
(iii)
0
,
5
6
a
(iv)
−
4
3
a
,
1
6
a
(v)
−
2
5
a
,
3
8
a
Question
5
5.
Solve :
(
x
−
9
)
(
x
−
4
)
+
(
x
−
6
)
(
x
−
8
)
=
41
21
(i)
(
65
,
12
)
(ii)
(
64
,
11
)
(iii)
(
61
,
9
)
(iv)
(
63
,
10
)
(v)
(
66
,
13
)
Question
6
6.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 45 . Find the three numbers.
(i)
11, 12, 13
(ii)
9, 10, 11
(iii)
7, 8, 9
(iv)
8, 9, 10
(v)
6, 7, 8
Question
7
7.
Solve :
(
x
2
−
4
x
)
2
−
14
(
x
2
−
4
x
)
+
49
=
0
(i)
(
4
+
√
11
)
,
(
4
−
√
11
)
,
(
5
+
√
11
)
,
(
4
−
√
11
)
(ii)
(
0
+
√
11
)
,
(
0
−
√
11
)
,
(
−
1
+
√
11
)
,
(
0
−
√
11
)
(iii)
(
2
+
√
11
)
,
(
2
−
√
11
)
,
(
2
+
√
11
)
,
(
2
−
√
11
)
(iv)
(
2
+
4
√
11
)
,
(
2
−
4
√
11
)
,
(
2
+
4
√
11
)
,
(
2
−
4
√
11
)
(v)
(
2
+
11
)
,
(
2
−
11
)
,
(
2
+
11
)
,
(
2
−
11
)
Question
8
8.
51 is divided into two parts such that the sum of their reciprocals is
51
440
.
Find the two parts
(i)
(
9
,
42
)
(ii)
(
11
,
40
)
(iii)
(
10
,
41
)
(iv)
(
13
,
38
)
(v)
(
12
,
39
)
Question
9
9.
The perimeter of a rectangular room is 26.00 m and the length of its diagonal is 9.85 m . Find the dimensions of the room
(i)
10.00 m , 3.00 m
(ii)
11.00 m , 2.00 m
(iii)
8.00 m , 5.00 m
(iv)
7.00 m , 6.00 m
(v)
9.00 m , 4.00 m
Question
10
10.
Solve the quadratic equation
x
−
7
=
−
6
x
(i)
(
7
,
1
)
(ii)
(
7
,
0
)
(iii)
(
9
,
0
)
(iv)
(
6
,
1
)
(v)
(
9
,
-2
)
Question
11
11.
The sum of the squares of two consecutive odd numbers is 514. Find the numbers
(i)
(-18)
,
(-16)
or
18
,
16
(ii)
(-19)
,
(-18)
or
19
,
18
(iii)
(-16)
,
(-14)
or
16
,
14
(iv)
(-14)
,
(-13)
or
14
,
13
(v)
(-17)
,
(-15)
or
17
,
15
Question
12
12.
Solve :
(
x
4
−
11
x
2
+
28
)
=
0
(i)
4
√
7
,
(
−
4
√
7
)
,
3
,
(
−
1
)
(ii)
7
,
(
−
7
)
,
1
,
(
−
3
)
(iii)
√
10
,
(
−
√
10
)
,
5
,
0
(iv)
√
7
,
(
−
√
7
)
,
2
,
(
−
2
)
(v)
√
5
,
(
−
√
4
)
,
0
,
(
−
4
)
Question
13
13.
Solve :
√
3
x
=
(
x
−
6
)
(i)
12
√
4
,
3
√
4
(ii)
12
,
3
(iii)
12
√
5
,
3
√
5
(iv)
12
√
3
,
3
√
3
(v)
12
√
2
,
3
√
2
Question
14
14.
A two digit number is such that the product of the digits is 18. When 27 is added to the number, the digits are reversed. Find the number
(i)
33
(ii)
35
(iii)
38
(iv)
37
(v)
36
Question
15
15.
Solve :
4
x
2
b
2
−
4
a
2
x
b
+
a
4
= 0
(i)
a
2
b
,
3
a
2
4
b
(ii)
a
2
3
b
,
3
a
2
8
b
(iii)
2
a
2
4
b
,
3
a
2
6
b
(iv)
0
,
a
2
6
b
(v)
a
2
b
,
5
a
2
6
b
Question
16
16.
Solve :
12
x
2
−
a
b
x
−
6
a
2
b
2
= 0
(i)
a
b
2
,
−
2
a
b
5
(ii)
3
a
b
2
,
−
2
a
b
(iii)
5
a
b
4
,
0
(iv)
3
a
b
4
,
−
2
a
b
3
(v)
a
b
4
,
−
4
a
b
3
Question
17
17.
The sum of the squares of two consecutive even numbers is 580. Find the numbers
(i)
(-19)
,
(-17)
or
19
,
17
(ii)
(-17)
,
(-15)
or
17
,
15
(iii)
(-15)
,
(-14)
or
15
,
14
(iv)
(-18)
,
(-16)
or
18
,
16
(v)
(-20)
,
(-19)
or
20
,
19
Question
18
18.
Find the number which exceeds its reciprocal by
2
2
3
(i)
2
(ii)
4
(iii)
1
(iv)
6
(v)
3
Question
19
19.
Find the roots of the quadratic equation
(
x
2
+
5
x
−
2
)
=
0
(i)
(
(
−
5
2
+
1
2
√
33
)
,
(
−
5
2
−
1
2
√
33
)
)
(ii)
(
(
−
3
2
+
1
2
√
33
)
,
(
−
7
2
−
1
2
√
33
)
)
(iii)
(
(
−
5
2
+
1
2
4
√
33
)
,
(
−
5
2
−
33
2
)
)
(iv)
(
(
−
3
2
+
1
2
√
33
)
,
(
−
5
2
−
33
2
)
)
(v)
(
(
−
5
2
+
1
2
4
√
33
)
,
(
−
5
2
−
1
2
√
33
)
)
Question
20
20.
The sum of the numerator and denominator of a fraction is
28
.
If
6
is added to both the numerator and denominator,
the fraction is increased by
36
391
. Find the fraction
(i)
9
17
(ii)
11
17
(iii)
11
15
(iv)
17
11
(v)
13
17
Question
21
21.
Solve :
(
x
+
8
)
(
x
+
9
)
(
x
+
10
)
(
x
+
11
)
=
5040
(i)
(
−
2
)
,
(
−
19
)
(ii)
0
,
(
−
17
)
(iii)
(
−
4
)
,
(
−
21
)
(iv)
(
−
1
)
,
(
−
18
)
(v)
2
,
(
−
16
)
Question
22
22.
Find the roots of the quadratic equation
(
27
x
2
−
15
x
+
2
)
=
0
(i)
(
1
,
2
7
)
(ii)
(
1
5
,
2
7
)
(iii)
(
1
,
0
)
(iv)
(
1
5
,
2
9
)
(v)
(
1
3
,
2
9
)
Question
23
23.
For what values of
k
are the roots of
(
k
−
13
)
x
2
+
(
k
+
8
)
x
+
(
k
−
37
)
=
0
equal
(i)
(
13
,
61
)
(ii)
(
11
,
61
)
(iii)
(
13
,
59
)
(iv)
(
10
,
62
)
(v)
(
11
,
62
)
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)
24
(ii)
22
(iii)
27
(iv)
25
(v)
23
Question
25
25.
Solve :
81
x
2
b
2
−
45
a
x
b
+
4
a
2
= 0
(i)
a
9
b
,
4
a
9
b
(ii)
−
a
9
b
,
2
a
9
b
(iii)
a
3
b
,
2
a
3
b
(iv)
a
11
b
,
4
a
11
b
(v)
a
7
b
,
4
a
7
b
Assignment Key
1) (iii)
2) (ii)
3) (v)
4) (i)
5) (ii)
6) (iv)
7) (iii)
8) (ii)
9) (v)
10) (iv)
11) (v)
12) (iv)
13) (ii)
14) (v)
15) (iii)
16) (iv)
17) (iv)
18) (v)
19) (i)
20) (ii)
21) (iv)
22) (v)
23) (iv)
24) (i)
25) (i)
