EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Find the discriminant of the quadratic equation
(
4
x
2
−
16
x
+
16
)
=
0
(i)
-2
(ii)
-1
(iii)
0
(iv)
3
(v)
1
Question
2
2.
The product of the roots of the quadratic equation
(
x
2
+
x
−
20
)
=
0
is
(i)
-22
(ii)
-20
(iii)
-19
(iv)
-18
(v)
-21
Question
3
3.
Find the quadratic equation whose roots are
(
7
−
6
√
2
)
and
(
7
+
6
√
2
)
(i)
(
2
x
2
−
14
x
−
23
)
=
0
(ii)
(
x
2
−
17
x
−
23
)
=
0
(iii)
(
x
2
−
11
x
−
23
)
=
0
(iv)
(
−
14
x
−
23
)
=
0
(v)
(
x
2
−
14
x
−
23
)
=
0
Question
4
4.
Find the roots of the quadratic equation correct to two decimal places
(
6
x
2
+
12
x
)
=
0
(i)
8.00 , 6.00
(ii)
7.00 , 5.00
(iii)
1.00 , 6.00
(iv)
0.00 , -2.00
(v)
2.00 , 0.00
Question
5
5.
Solve :
35
x
2
−
25
a
x
+
14
x
−
10
a
= 0
(i)
a
,
0
(ii)
3
a
7
,
−
4
5
(iii)
a
,
−
2
3
(iv)
5
a
9
,
−
2
7
(v)
5
a
7
,
−
2
5
Question
6
6.
Find the discriminant of the quadratic equation
(
x
2
−
4
x
−
5
)
=
0
(i)
33
(ii)
39
(iii)
37
(iv)
35
(v)
36
Question
7
7.
Solve :
2
x
2
+
14
√
2
x
+
48
=
0
(i)
(
−
8
)
√
8
,
(
−
6
)
√
8
(ii)
(
−
8
)
√
2
,
(
−
6
)
√
2
(iii)
(
−
8
√
4
)
√
2
,
(
−
6
√
4
)
√
2
(iv)
(
−
8
√
4
)
√
2
,
(
−
6
)
√
2
(v)
(
−
8
)
√
2
,
(
−
6
)
√
8
Question
8
8.
Solve :
72
x
2
a
4
−
5
b
x
a
2
−
12
b
2
= 0
(i)
4
b
7
a
2
,
−
b
2
a
2
(ii)
4
b
11
a
2
,
−
3
b
10
a
2
(iii)
4
b
9
a
2
,
−
3
b
8
a
2
(iv)
2
b
9
a
2
,
−
5
b
8
a
2
(v)
2
b
3
a
2
,
−
b
8
a
2
Question
9
9.
For what values of
k
are the roots of
(
k
−
1
)
x
2
+
(
k
+
44
)
x
+
(
k
+
23
)
=
0
equal
(i)
(
(
−
26
)
,
26
)
(ii)
(
(
−
23
)
,
25
)
(iii)
(
(
−
23
)
,
23
)
(iv)
(
(
−
25
)
,
25
)
(v)
(
(
−
25
)
,
26
)
Question
10
10.
Solve :
35
x
2
b
2
+
37
a
x
b
+
6
a
2
= 0
(i)
a
5
b
,
−
4
a
7
b
(ii)
−
a
7
b
,
−
2
a
3
b
(iii)
−
a
5
b
,
−
6
a
7
b
(iv)
−
a
3
b
,
−
6
a
5
b
(v)
−
3
a
5
b
,
−
8
a
7
b
Question
11
11.
Solve the quadratic equation
x
+
10
x
=
7
(i)
(
6
,
2
)
(ii)
(
6
,
1
)
(iii)
(
5
,
2
)
(iv)
(
8
,
1
)
(v)
(
8
,
-1
)
Question
12
12.
Solve :
6
x
2
+
a
b
2
x
−
2
a
2
b
4
= 0
(i)
−
2
a
b
2
3
,
a
b
2
2
(ii)
0
,
3
a
b
2
2
(iii)
−
2
a
b
2
,
a
b
2
(iv)
−
4
a
b
2
3
,
−
a
b
2
2
(v)
−
2
a
b
2
5
,
a
b
2
4
Question
13
13.
Solve :
(
x
−
11
)
(
x
−
2
)
+
(
x
−
8
)
(
x
−
10
)
=
61
33
(i)
(
136
3
,
12
)
(ii)
(
224
5
,
11
)
(iii)
(
228
5
,
16
)
(iv)
(
316
7
,
14
)
(v)
(
226
5
,
13
)
Question
14
14.
Find the quadratic equation with roots
(
-3
,
-3
)
(i)
(
x
2
+
9
x
+
18
)
=
0
(ii)
(
x
2
+
6
x
+
9
)
=
0
(iii)
(
x
2
+
5
x
+
6
)
=
0
(iv)
(
x
2
+
7
x
+
12
)
=
0
(v)
(
x
2
+
3
x
)
=
0
Question
15
15.
Solve :
24
x
2
+
a
b
2
x
−
10
a
2
b
4
= 0
(i)
3
a
b
2
8
,
−
4
a
b
2
3
(ii)
a
b
2
2
,
−
2
a
b
2
5
(iii)
5
a
b
2
6
,
−
2
a
b
2
(iv)
5
a
b
2
8
,
−
2
a
b
2
3
(v)
7
a
b
2
8
,
0
Question
16
16.
Find the discriminant of the quadratic equation
(
x
2
−
4
x
+
13
)
=
0
(i)
-35
(ii)
-34
(iii)
-38
(iv)
-37
(v)
-36
Question
17
17.
Find the roots of the quadratic equation
(
x
2
+
15
x
+
56
)
=
0
(i)
(
-7
,
-8
)
(ii)
(
-6
,
-9
)
(iii)
(
-5
,
-9
)
(iv)
(
-6
,
-8
)
(v)
(
-5
,
-10
)
Question
18
18.
Solve :
63
x
2
−
83
a
2
b
x
+
24
a
4
b
2
= 0
(i)
10
a
2
b
9
,
5
a
2
b
7
(ii)
8
a
2
b
9
,
3
a
2
b
7
(iii)
8
a
2
b
7
,
3
a
2
b
5
(iv)
8
a
2
b
11
,
a
2
b
3
(v)
2
a
2
b
3
,
a
2
b
7
Question
19
19.
Solve :
12
x
2
a
2
−
4
x
a
−
1
= 0
(i)
1
6
a
,
1
a
(ii)
−
1
4
a
,
1
a
(iii)
−
1
2
a
,
0
(iv)
−
1
8
a
,
1
3
a
(v)
−
1
6
a
,
2
4
a
Question
20
20.
Solve :
24
x
2
b
2
−
22
x
b
+
3
= 0
(i)
1
2
b
,
−
1
6
b
(ii)
1
b
,
1
4
b
(iii)
6
8
b
,
1
6
b
(iv)
3
5
b
,
1
8
b
(v)
1
b
,
1
2
b
Question
21
21.
Solve :
15
x
2
b
+
6
x
b
−
10
x
−
4
= 0
(i)
−
2
5
,
2
3
b
(ii)
0
,
4
3
b
(iii)
−
2
7
,
2
5
b
(iv)
−
4
5
,
0
(v)
−
2
3
,
2
b
Question
22
22.
Find the quadratic equation, the sum of whose roots is
-11
and product is
30
(i)
(
x
2
+
11
x
+
30
)
=
0
(ii)
(
2
x
2
+
11
x
+
30
)
=
0
(iii)
(
11
x
+
30
)
=
0
(iv)
(
x
2
+
13
x
+
30
)
=
0
(v)
(
x
2
+
8
x
+
30
)
=
0
Question
23
23.
Solve :
(
x
2
−
4
x
)
2
−
15
(
x
2
−
4
x
)
+
54
=
0
(i)
(
2
+
4
√
13
)
,
(
2
−
4
√
13
)
,
(
2
+
4
√
10
)
,
(
2
−
4
√
10
)
(ii)
(
0
+
√
13
)
,
(
0
−
√
13
)
,
(
0
+
√
10
)
,
(
−
1
−
√
10
)
(iii)
(
4
+
√
13
)
,
(
5
−
√
13
)
,
(
4
+
√
10
)
,
(
4
−
√
10
)
(iv)
(
2
+
13
)
,
(
2
−
13
)
,
(
2
+
10
)
,
(
2
−
10
)
(v)
(
2
+
√
13
)
,
(
2
−
√
13
)
,
(
2
+
√
10
)
,
(
2
−
√
10
)
Question
24
24.
Find the roots of the quadratic equation
(
35
x
2
−
17
x
+
2
)
=
0
(i)
(
4
7
,
1
3
)
(ii)
(
2
9
,
1
3
)
(iii)
(
2
7
,
1
5
)
(iv)
(
4
7
,
(
-1
5
)
)
(v)
(
2
9
,
1
5
)
Question
25
25.
The product of the roots of the quadratic equation
(
16
x
2
−
72
x
+
81
)
=
0
is
(i)
71
14
(ii)
79
16
(iii)
91
18
(iv)
81
16
(v)
83
16
Assignment Key
1) (iii)
2) (ii)
3) (v)
4) (iv)
5) (v)
6) (v)
7) (ii)
8) (iii)
9) (i)
10) (iii)
11) (iii)
12) (i)
13) (v)
14) (ii)
15) (iv)
16) (v)
17) (i)
18) (ii)
19) (v)
20) (iii)
21) (i)
22) (i)
23) (v)
24) (iii)
25) (iv)
