EduSahara™ Assignment
Name : Zeroes of a Cubic Polynomial
Chapter : Polynomials
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
If
α, β, γ
are the roots of the cubic equation
(
140
x
3
−
451
x
2
+
338
x
−
72
)
=
0
,
find
α + β + γ
(i)
451
140
(ii)
169
70
(iii)
(
−
451
140
)
(iv)
(
−
169
70
)
(v)
(
−
18
35
)
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
72
x
3
−
183
x
2
+
137
x
−
28
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
137
72
)
(ii)
61
24
(iii)
137
72
(iv)
7
18
(v)
(
−
7
18
)
Question
3
3.
If
α, β, γ
are the roots of the cubic equation
(
126
x
3
−
269
x
2
+
187
x
−
42
)
=
0
,
find
αβγ
(i)
1
3
(ii)
187
126
(iii)
(
−
187
126
)
(iv)
(
−
1
3
)
(v)
269
126
Question
4
4.
If one of the roots of the cubic equation
(
175
x
3
−
785
x
2
+
1161
x
−
567
)
=
0
is
9
7
,
find the remaining real roots
(i)
(
7
5
,
9
5
)
(ii)
(
1
,
1
)
(iii)
(
11
7
,
9
5
)
(iv)
(
11
9
,
9
7
)
(v)
(
7
5
,
5
3
)
Question
5
5.
If one of the roots of the cubic equation
(
x
3
+
4
x
2
−
41
x
+
36
)
=
0
is
4
,
find the remaining real roots
(i)
(
3
,
0
)
(ii)
(
1
,
(
−
1
)
)
(iii)
(
6
,
4
)
(iv)
(
1
,
(
−
9
)
)
(v)
(
5
,
2
)
Question
6
6.
If
α
=
8
9
,
β
=
3
8
,
γ
=
4
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
109
54
)
(ii)
(
−
187
72
)
(iii)
109
54
(iv)
(
−
4
9
)
(v)
4
9
Question
7
7.
If
α
=
7
3
,
β
=
3
2
,
γ
=
2
9
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
(
−
235
54
)
(ii)
73
18
(iii)
7
9
(iv)
235
54
(v)
(
−
7
9
)
Question
8
8.
If
α
=
3
2
,
β
=
5
9
,
γ
=
2
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
179
126
)
(ii)
295
126
(iii)
5
21
(iv)
(
−
295
126
)
(v)
(
−
5
21
)
Question
9
9.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
−
2
x
−
6
,
find the value of
a
(i)
(-5)
(ii)
(-2)
(iii)
(-3)
(iv)
(-4)
(v)
(-1)
Question
10
10.
If
α, β, γ
are the roots of the cubic equation
(
75
x
3
−
110
x
2
+
49
x
−
6
)
=
0
,
find
α + β + γ
(i)
49
75
(ii)
(
−
22
15
)
(iii)
2
25
(iv)
22
15
(v)
(
−
49
75
)
Question
11
11.
If
α, β, γ
are the roots of the cubic equation
(
135
x
3
−
528
x
2
+
496
x
−
128
)
=
0
,
find
αβ + βγ + γα
(i)
128
135
(ii)
496
135
(iii)
(
−
496
135
)
(iv)
(
−
128
135
)
(v)
(
−
176
45
)
Question
12
12.
If
α, β, γ
are the roots of the cubic equation
(
42
x
3
−
221
x
2
+
332
x
−
105
)
=
0
,
find
αβγ
(i)
(
−
221
42
)
(ii)
(
−
166
21
)
(iii)
166
21
(iv)
5
2
(v)
(
−
5
2
)
Question
13
13.
If one of the roots of the cubic equation
(
50
x
3
−
125
x
2
+
82
x
−
16
)
=
0
is
2
5
,
find the remaining real roots
(i)
(
2
3
,
2
)
(ii)
(
4
5
,
2
)
(iii)
(
0
,
6
5
)
(iv)
(
8
5
,
1
2
)
(v)
(
2
7
,
10
7
)
Question
14
14.
If one of the roots of the cubic equation
(
x
3
−
37
x
−
84
)
=
0
is
(
−
3
)
,
find the remaining real roots
(i)
(
(
−
6
)
,
(
−
6
)
)
(ii)
(
(
−
1
)
,
(
−
2
)
)
(iii)
(
(
−
4
)
,
(
−
5
)
)
(iv)
(
(
−
4
)
,
7
)
(v)
(
(
−
2
)
,
(
−
3
)
)
Question
15
15.
If
α
=
5
8
,
β
=
2
5
,
γ
=
2
5
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
57
40
)
(ii)
(
−
33
50
)
(iii)
(
−
1
10
)
(iv)
1
10
(v)
33
50
Question
16
16.
If
α
=
7
8
,
β
=
1
6
,
γ
=
3
8
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
7
128
(ii)
17
12
(iii)
(
−
17
12
)
(iv)
(
−
103
192
)
(v)
103
192
Question
17
17.
If
α
=
7
4
,
β
=
4
3
,
γ
=
7
2
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
49
6
)
(ii)
(
−
105
8
)
(iii)
105
8
(iv)
(
−
79
12
)
(v)
79
12
Assignment Key
1) (i)
2) (iii)
3) (i)
4) (i)
5) (iv)
6) (ii)
7) (iv)
8) (v)
9) (iii)
10) (iv)
11) (ii)
12) (iv)
13) (iv)
14) (iv)
15) (i)
16) (v)
17) (i)
