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
(
315
x
3
−
743
x
2
+
538
x
−
120
)
=
0
,
find
α + β + γ
(i)
(
−
8
21
)
(ii)
8
21
(iii)
743
315
(iv)
(
−
538
315
)
(v)
(
−
743
315
)
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
50
x
3
−
225
x
2
+
298
x
−
120
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
149
25
)
(ii)
12
5
(iii)
9
2
(iv)
149
25
(v)
(
−
12
5
)
Question
3
3.
If
α, β, γ
are the roots of the cubic equation
(
54
x
3
−
285
x
2
+
368
x
−
112
)
=
0
,
find
αβγ
(i)
(
−
56
27
)
(ii)
(
−
95
18
)
(iii)
(
−
184
27
)
(iv)
95
18
(v)
56
27
Question
4
4.
If one of the roots of the cubic equation
(
120
x
3
−
493
x
2
+
560
x
−
147
)
=
0
is
7
3
,
find the remaining real roots
(i)
(
11
5
,
9
7
)
(ii)
(
5
3
,
1
)
(iii)
(
3
,
5
3
)
(iv)
(
7
5
,
3
8
)
(v)
(
3
,
9
5
)
Question
5
5.
If one of the roots of the cubic equation
(
x
3
−
49
x
−
120
)
=
0
is
8
,
find the remaining real roots
(i)
(
7
,
(
−
4
)
)
(ii)
(
5
,
(
−
6
)
)
(iii)
(
9
,
(
−
2
)
)
(iv)
(
11
,
0
)
(v)
(
(
−
3
)
,
(
−
5
)
)
Question
6
6.
If
α
=
5
7
,
β
=
7
5
,
γ
=
3
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
89
35
(ii)
(
−
3
7
)
(iii)
467
245
(iv)
(
−
89
35
)
(v)
3
7
Question
7
7.
If
α
=
3
7
,
β
=
1
2
,
γ
=
1
6
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
31
84
(ii)
23
21
(iii)
(
−
1
28
)
(iv)
(
−
31
84
)
(v)
1
28
Question
8
8.
If
α
=
5
2
,
β
=
1
4
,
γ
=
7
4
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
87
16
(ii)
(
−
87
16
)
(iii)
(
−
35
32
)
(iv)
(
−
9
2
)
(v)
35
32
Question
9
9.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
+
4
x
+
12
,
find the value of
a
(i)
(-1)
(ii)
(-2)
(iii)
(-3)
(iv)
(-4)
(v)
(-6)
Question
10
10.
If
α, β, γ
are the roots of the cubic equation
(
243
x
3
−
756
x
2
+
471
x
−
70
)
=
0
,
find
α + β + γ
(i)
(
−
157
81
)
(ii)
157
81
(iii)
70
243
(iv)
(
−
28
9
)
(v)
28
9
Question
11
11.
If
α, β, γ
are the roots of the cubic equation
(
30
x
3
−
41
x
2
+
17
x
−
2
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
1
15
)
(ii)
(
−
17
30
)
(iii)
17
30
(iv)
1
15
(v)
(
−
41
30
)
Question
12
12.
If
α, β, γ
are the roots of the cubic equation
(
100
x
3
−
345
x
2
+
347
x
−
90
)
=
0
,
find
αβγ
(i)
(
−
69
20
)
(ii)
9
10
(iii)
(
−
9
10
)
(iv)
(
−
347
100
)
(v)
347
100
Question
13
13.
If one of the roots of the cubic equation
(
40
x
3
−
214
x
2
+
275
x
−
56
)
=
0
is
1
4
,
find the remaining real roots
(i)
(
(
−
1
4
)
,
5
2
)
(ii)
(
1
2
,
4
)
(iii)
(
1
6
,
13
4
)
(iv)
(
7
2
,
8
5
)
(v)
(
3
4
,
9
2
)
Question
14
14.
If one of the roots of the cubic equation
(
x
3
+
13
x
2
+
54
x
+
72
)
=
0
is
(
−
4
)
,
find the remaining real roots
(i)
(
(
−
3
)
,
(
−
6
)
)
(ii)
(
(
−
6
)
,
(
−
6
)
)
(iii)
(
(
−
1
)
,
(
−
1
)
)
(iv)
(
(
−
5
)
,
(
−
4
)
)
(v)
(
(
−
3
)
,
(
−
2
)
)
Question
15
15.
If
α
=
1
6
,
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)
(
−
19
54
)
(ii)
(
−
133
90
)
(iii)
(
−
1
45
)
(iv)
1
45
(v)
133
90
Question
16
16.
If
α
=
7
4
,
β
=
3
8
,
γ
=
8
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
691
224
(ii)
(
−
3
4
)
(iii)
(
−
691
224
)
(iv)
183
56
(v)
3
4
Question
17
17.
If
α
=
5
4
,
β
=
5
7
,
γ
=
5
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
125
196
)
(ii)
225
98
(iii)
(
−
225
98
)
(iv)
125
196
(v)
(
−
75
28
)
Question
18
18.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
+
9
x
+
45
,
find the value of
a
(i)
(-6)
(ii)
(-3)
(iii)
(-4)
(iv)
(-5)
(v)
(-8)
Assignment Key
1) (iii)
2) (iv)
3) (v)
4) (iv)
5) (v)
6) (iv)
7) (i)
8) (iii)
9) (iii)
10) (v)
11) (iii)
12) (ii)
13) (iv)
14) (i)
15) (ii)
16) (i)
17) (i)
18) (iv)
