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
−
439
x
2
+
438
x
−
135
)
=
0
,
find
α + β + γ
(i)
(
−
219
70
)
(ii)
27
28
(iii)
(
−
439
140
)
(iv)
219
70
(v)
439
140
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
30
x
3
−
187
x
2
+
378
x
−
245
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
63
5
)
(ii)
63
5
(iii)
(
−
49
6
)
(iv)
187
30
(v)
49
6
Question
3
3.
If
α, β, γ
are the roots of the cubic equation
(
315
x
3
−
482
x
2
+
224
x
−
32
)
=
0
,
find
αβγ
(i)
(
−
32
315
)
(ii)
32
315
(iii)
(
−
482
315
)
(iv)
(
−
32
45
)
(v)
32
45
Question
4
4.
If one of the roots of the cubic equation
(
96
x
3
−
260
x
2
+
203
x
−
36
)
=
0
is
9
8
,
find the remaining real roots
(i)
(
7
6
,
2
)
(ii)
(
7
8
,
2
3
)
(iii)
(
11
8
,
2
)
(iv)
(
11
10
,
6
5
)
(v)
(
4
3
,
1
4
)
Question
5
5.
If one of the roots of the cubic equation
(
x
3
−
19
x
2
+
111
x
−
189
)
=
0
is
9
,
find the remaining real roots
(i)
(
12
,
6
)
(ii)
(
7
,
0
)
(iii)
(
10
,
4
)
(iv)
(
3
,
7
)
(v)
(
8
,
2
)
Question
6
6.
If
α
=
5
6
,
β
=
5
8
,
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)
(
−
125
336
)
(ii)
25
16
(iii)
(
−
25
16
)
(iv)
(
−
365
168
)
(v)
365
168
Question
7
7.
If
α
=
2
9
,
β
=
9
2
,
γ
=
1
8
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
229
144
(ii)
(
−
1
8
)
(iii)
1
8
(iv)
349
72
(v)
(
−
349
72
)
Question
8
8.
If
α
=
5
2
,
β
=
2
5
,
γ
=
5
9
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
5
9
(ii)
(
−
47
18
)
(iii)
(
−
311
90
)
(iv)
(
−
5
9
)
(v)
47
18
Question
9
9.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
−
3
x
−
3
,
find the value of
a
(i)
0
(ii)
(-3)
(iii)
(-2)
(iv)
2
(v)
(-1)
Question
10
10.
If
α, β, γ
are the roots of the cubic equation
(
75
x
3
−
100
x
2
+
37
x
−
4
)
=
0
,
find
α + β + γ
(i)
4
3
(ii)
(
−
37
75
)
(iii)
4
75
(iv)
37
75
(v)
(
−
4
75
)
Question
11
11.
If
α, β, γ
are the roots of the cubic equation
(
63
x
3
−
324
x
2
+
512
x
−
256
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
36
7
)
(ii)
256
63
(iii)
512
63
(iv)
36
7
(v)
(
−
256
63
)
Question
12
12.
If
α, β, γ
are the roots of the cubic equation
(
56
x
3
−
386
x
2
+
809
x
−
504
)
=
0
,
find
αβγ
(i)
(
−
809
56
)
(ii)
809
56
(iii)
(
−
9
)
(iv)
9
(v)
193
28
Question
13
13.
If one of the roots of the cubic equation
(
84
x
3
−
307
x
2
+
344
x
−
112
)
=
0
is
4
7
,
find the remaining real roots
(i)
(
2
7
,
5
4
)
(ii)
(
4
9
,
3
2
)
(iii)
(
7
4
,
4
3
)
(iv)
(
6
7
,
9
4
)
(v)
(
4
5
,
5
2
)
Question
14
14.
If one of the roots of the cubic equation
(
x
3
−
16
x
2
+
75
x
−
108
)
=
0
is
4
,
find the remaining real roots
(i)
(
3
,
9
)
(ii)
(
3
,
2
)
(iii)
(
7
,
5
)
(iv)
(
5
,
4
)
(v)
(
2
,
0
)
Question
15
15.
If
α
=
7
2
,
β
=
5
6
,
γ
=
5
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
175
36
(ii)
(
−
6
)
(iii)
(
−
175
36
)
(iv)
365
36
(v)
6
Question
16
16.
If
α
=
1
2
,
β
=
5
6
,
γ
=
9
2
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
(
−
15
8
)
(ii)
15
8
(iii)
(
−
77
12
)
(iv)
(
−
35
6
)
(v)
77
12
Question
17
17.
If
α
=
5
9
,
β
=
5
9
,
γ
=
1
2
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
25
162
(ii)
(
−
70
81
)
(iii)
70
81
(iv)
(
−
25
162
)
(v)
(
−
29
18
)
Assignment Key
1) (v)
2) (ii)
3) (ii)
4) (v)
5) (iv)
6) (iv)
7) (i)
8) (iv)
9) (v)
10) (i)
11) (iii)
12) (iv)
13) (iii)
14) (i)
15) (ii)
16) (v)
17) (iv)
