EduSahara™ Assignment
Name : Cubic Polynomials
Chapter : Polynomials
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
If
α, β, γ
are the roots of the cubic equation
(
50
x
3
−
185
x
2
+
213
x
−
72
)
=
0
,
find
α + β + γ
(i)
36
25
(ii)
37
10
(iii)
(
−
213
50
)
(iv)
(
−
36
25
)
(v)
213
50
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
105
x
3
−
401
x
2
+
400
x
−
84
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
80
21
)
(ii)
(
−
4
5
)
(iii)
80
21
(iv)
401
105
(v)
(
−
401
105
)
Question
3
3.
If
α, β, γ
are the roots of the cubic equation
(
160
x
3
−
196
x
2
+
75
x
−
9
)
=
0
,
find
αβγ
(i)
9
160
(ii)
(
−
9
160
)
(iii)
(
−
49
40
)
(iv)
49
40
(v)
15
32
Question
4
4.
If one of the roots of the cubic equation
(
48
x
3
−
220
x
2
+
300
x
−
125
)
=
0
is
5
4
,
find the remaining real roots
(i)
(
3
2
,
3
)
(ii)
(
7
4
,
7
2
)
(iii)
(
3
4
,
3
2
)
(iv)
(
5
2
,
5
6
)
(v)
(
7
6
,
9
4
)
Question
5
5.
If one of the roots of the cubic equation
(
x
3
−
3
x
2
−
81
x
+
243
)
=
0
is
9
,
find the remaining real roots
(i)
(
7
,
0
)
(ii)
(
10
,
4
)
(iii)
(
12
,
6
)
(iv)
(
8
,
2
)
(v)
(
3
,
(
−
9
)
)
Question
6
6.
If
α
=
1
8
,
β
=
5
4
,
γ
=
5
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
255
224
)
(ii)
25
224
(iii)
117
56
(iv)
(
−
25
224
)
(v)
(
−
117
56
)
Question
7
7.
If
α
=
2
3
,
β
=
1
5
,
γ
=
1
2
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
41
30
(ii)
(
−
1
15
)
(iii)
17
30
(iv)
(
−
17
30
)
(v)
(
−
41
30
)
Question
8
8.
If
α
=
5
7
,
β
=
3
5
,
γ
=
5
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
55
21
)
(ii)
(
−
313
105
)
(iii)
55
21
(iv)
(
−
5
7
)
(v)
313
105
Question
9
9.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
−
5
x
−
10
,
find the value of
a
(i)
1
(ii)
(-4)
(iii)
(-1)
(iv)
(-2)
(v)
(-3)
Question
10
10.
If
α, β, γ
are the roots of the cubic equation
(
216
x
3
−
555
x
2
+
463
x
−
126
)
=
0
,
find
α + β + γ
(i)
(
−
463
216
)
(ii)
463
216
(iii)
7
12
(iv)
(
−
185
72
)
(v)
185
72
Question
11
11.
If
α, β, γ
are the roots of the cubic equation
(
12
x
3
−
64
x
2
+
85
x
−
28
)
=
0
,
find
αβ + βγ + γα
(i)
7
3
(ii)
(
−
16
3
)
(iii)
(
−
7
3
)
(iv)
85
12
(v)
16
3
Question
12
12.
If
α, β, γ
are the roots of the cubic equation
(
378
x
3
−
681
x
2
+
355
x
−
42
)
=
0
,
find
αβγ
(i)
1
9
(ii)
355
378
(iii)
(
−
1
9
)
(iv)
227
126
(v)
(
−
355
378
)
Question
13
13.
If one of the roots of the cubic equation
(
50
x
3
−
125
x
2
+
83
x
−
12
)
=
0
is
3
2
,
find the remaining real roots
(i)
(
5
4
,
4
7
)
(ii)
(
4
5
,
1
5
)
(iii)
(
2
,
4
3
)
(iv)
(
5
2
,
6
5
)
(v)
(
1
2
,
2
5
)
Question
14
14.
If one of the roots of the cubic equation
(
x
3
−
12
x
2
+
41
x
−
42
)
=
0
is
7
,
find the remaining real roots
(i)
(
9
,
4
)
(ii)
(
2
,
3
)
(iii)
(
6
,
1
)
(iv)
(
5
,
0
)
(v)
(
8
,
3
)
Question
15
15.
If
α
=
4
7
,
β
=
1
9
,
γ
=
6
5
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
278
315
)
(ii)
8
105
(iii)
593
315
(iv)
(
−
593
315
)
(v)
278
315
Question
16
16.
If
α
=
2
9
,
β
=
9
7
,
γ
=
4
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
(
−
506
441
)
(ii)
131
63
(iii)
506
441
(iv)
8
49
(v)
(
−
131
63
)
Question
17
17.
If
α
=
7
4
,
β
=
2
9
,
γ
=
1
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
7
54
)
(ii)
83
36
(iii)
(
−
83
36
)
(iv)
113
108
(v)
(
−
113
108
)
Question
18
18.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
+
8
x
+
8
,
find the value of
a
(i)
(-1)
(ii)
0
(iii)
(-2)
(iv)
(-3)
(v)
2
Assignment Key
1) (ii)
2) (iii)
3) (i)
4) (iv)
5) (v)
6) (v)
7) (iii)
8) (iv)
9) (iv)
10) (v)
11) (iv)
12) (i)
13) (ii)
14) (ii)
15) (iv)
16) (iii)
17) (i)
18) (i)
