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
(
280
x
3
−
383
x
2
+
154
x
−
15
)
=
0
,
find
α + β + γ
(i)
11
20
(ii)
383
280
(iii)
(
−
383
280
)
(iv)
(
−
3
56
)
(v)
3
56
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
378
x
3
−
453
x
2
+
127
x
−
10
)
=
0
,
find
αβ + βγ + γα
(i)
127
378
(ii)
(
−
127
378
)
(iii)
151
126
(iv)
5
189
(v)
(
−
5
189
)
Question
3
3.
If
α, β, γ
are the roots of the cubic equation
(
98
x
3
−
455
x
2
+
633
x
−
270
)
=
0
,
find
αβγ
(i)
(
−
65
14
)
(ii)
135
49
(iii)
65
14
(iv)
(
−
633
98
)
(v)
633
98
Question
4
4.
If one of the roots of the cubic equation
(
40
x
3
−
66
x
2
+
35
x
−
6
)
=
0
is
3
4
,
find the remaining real roots
(i)
(
5
4
,
3
2
)
(ii)
(
3
2
,
1
)
(iii)
(
1
2
,
1
4
)
(iv)
(
1
4
,
(
−
1
2
)
)
(v)
(
1
2
,
2
5
)
Question
5
5.
If one of the roots of the cubic equation
(
x
3
+
2
x
2
−
x
−
2
)
=
0
is
1
,
find the remaining real roots
(i)
(
(
−
1
)
,
(
−
2
)
)
(ii)
(
(
−
1
)
,
(
−
4
)
)
(iii)
(
2
,
0
)
(iv)
(
3
,
1
)
(v)
(
0
,
(
−
2
)
)
Question
6
6.
If
α
=
7
2
,
β
=
3
7
,
γ
=
3
5
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
27
7
)
(ii)
(
−
317
70
)
(iii)
27
7
(iv)
9
10
(v)
317
70
Question
7
7.
If
α
=
1
8
,
β
=
8
5
,
γ
=
8
9
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
26
15
(ii)
8
45
(iii)
941
360
(iv)
(
−
26
15
)
(v)
(
−
8
45
)
Question
8
8.
If
α
=
2
3
,
β
=
7
8
,
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)
(
−
379
168
)
(ii)
379
168
(iii)
(
−
5
12
)
(iv)
(
−
283
168
)
(v)
283
168
Question
9
9.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
+
7
x
+
21
,
find the value of
a
(i)
(-2)
(ii)
(-4)
(iii)
(-3)
(iv)
(-1)
(v)
(-6)
Question
10
10.
If
α, β, γ
are the roots of the cubic equation
(
189
x
3
−
282
x
2
+
119
x
−
10
)
=
0
,
find
α + β + γ
(i)
17
27
(ii)
(
−
10
189
)
(iii)
94
63
(iv)
(
−
94
63
)
(v)
10
189
Question
11
11.
If
α, β, γ
are the roots of the cubic equation
(
225
x
3
−
385
x
2
+
148
x
−
12
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
4
75
)
(ii)
(
−
148
225
)
(iii)
4
75
(iv)
(
−
77
45
)
(v)
148
225
Question
12
12.
If
α, β, γ
are the roots of the cubic equation
(
24
x
3
−
98
x
2
+
51
x
−
7
)
=
0
,
find
αβγ
(i)
49
12
(ii)
7
24
(iii)
17
8
(iv)
(
−
49
12
)
(v)
(
−
17
8
)
Question
13
13.
If one of the roots of the cubic equation
(
378
x
3
−
579
x
2
+
173
x
−
14
)
=
0
is
1
7
,
find the remaining real roots
(i)
(
2
9
,
7
6
)
(ii)
(
1
5
,
2
7
)
(iii)
(
1
9
,
2
11
)
(iv)
(
(
−
1
7
)
,
0
)
(v)
(
3
7
,
4
9
)
Question
14
14.
If one of the roots of the cubic equation
(
x
3
−
3
x
2
−
46
x
+
48
)
=
0
is
(
−
6
)
,
find the remaining real roots
(i)
(
(
−
8
)
,
5
)
(ii)
(
8
,
1
)
(iii)
(
(
−
4
)
,
10
)
(iv)
(
(
−
5
)
,
9
)
(v)
(
(
−
7
)
,
7
)
Question
15
15.
If
α
=
5
7
,
β
=
5
7
,
γ
=
2
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
12
7
(ii)
(
−
45
49
)
(iii)
(
−
50
343
)
(iv)
(
−
12
7
)
(v)
45
49
Question
16
16.
If
α
=
1
9
,
β
=
3
7
,
γ
=
3
4
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
325
252
(ii)
(
−
19
42
)
(iii)
(
−
1
28
)
(iv)
19
42
(v)
1
28
Question
17
17.
If
α
=
1
4
,
β
=
8
3
,
γ
=
9
4
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
3
2
(ii)
(
−
31
6
)
(iii)
31
6
(iv)
(
−
347
48
)
(v)
(
−
3
2
)
Assignment Key
1) (ii)
2) (i)
3) (ii)
4) (v)
5) (i)
6) (ii)
7) (i)
8) (iii)
9) (iii)
10) (iii)
11) (v)
12) (ii)
13) (i)
14) (ii)
15) (iv)
16) (iv)
17) (v)
