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
(
42
x
3
−
283
x
2
+
463
x
−
180
)
=
0
,
find
α + β + γ
(i)
(
−
283
42
)
(ii)
283
42
(iii)
(
−
30
7
)
(iv)
463
42
(v)
(
−
463
42
)
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
63
x
3
−
381
x
2
+
688
x
−
320
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
127
21
)
(ii)
688
63
(iii)
(
−
688
63
)
(iv)
(
−
320
63
)
(v)
320
63
Question
3
3.
If
α, β, γ
are the roots of the cubic equation
(
256
x
3
−
960
x
2
+
1148
x
−
441
)
=
0
,
find
αβγ
(i)
15
4
(ii)
(
−
15
4
)
(iii)
441
256
(iv)
(
−
287
64
)
(v)
287
64
Question
4
4.
If one of the roots of the cubic equation
(
90
x
3
−
341
x
2
+
421
x
−
168
)
=
0
is
8
9
,
find the remaining real roots
(i)
(
8
11
,
9
7
)
(ii)
(
10
9
,
9
5
)
(iii)
(
7
5
,
3
2
)
(iv)
(
2
3
,
1
)
(v)
(
8
7
,
5
3
)
Question
5
5.
If one of the roots of the cubic equation
(
x
3
−
2
x
2
−
71
x
+
252
)
=
0
is
4
,
find the remaining real roots
(i)
(
2
,
(
−
12
)
)
(ii)
(
3
,
(
−
10
)
)
(iii)
(
6
,
(
−
7
)
)
(iv)
(
(
−
9
)
,
7
)
(v)
(
5
,
(
−
8
)
)
Question
6
6.
If
α
=
5
2
,
β
=
2
7
,
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)
6
7
(ii)
279
70
(iii)
(
−
142
35
)
(iv)
(
−
279
70
)
(v)
142
35
Question
7
7.
If
α
=
9
5
,
β
=
1
5
,
γ
=
7
9
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
25
9
(ii)
7
25
(iii)
(
−
431
225
)
(iv)
431
225
(v)
(
−
7
25
)
Question
8
8.
If
α
=
7
8
,
β
=
1
5
,
γ
=
7
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
409
120
)
(ii)
161
60
(iii)
49
120
(iv)
(
−
49
120
)
(v)
409
120
Question
9
9.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
−
3
x
−
15
,
find the value of
a
(i)
(-3)
(ii)
(-6)
(iii)
(-5)
(iv)
(-7)
(v)
(-4)
Question
10
10.
If
α, β, γ
are the roots of the cubic equation
(
42
x
3
−
179
x
2
+
216
x
−
63
)
=
0
,
find
α + β + γ
(i)
(
−
36
7
)
(ii)
3
2
(iii)
179
42
(iv)
(
−
179
42
)
(v)
36
7
Question
11
11.
If
α, β, γ
are the roots of the cubic equation
(
441
x
3
−
1316
x
2
+
1243
x
−
360
)
=
0
,
find
αβ + βγ + γα
(i)
188
63
(ii)
(
−
188
63
)
(iii)
1243
441
(iv)
(
−
1243
441
)
(v)
40
49
Question
12
12.
If
α, β, γ
are the roots of the cubic equation
(
45
x
3
−
159
x
2
+
110
x
−
16
)
=
0
,
find
αβγ
(i)
22
9
(ii)
(
−
16
45
)
(iii)
53
15
(iv)
16
45
(v)
(
−
22
9
)
Question
13
13.
If one of the roots of the cubic equation
(
90
x
3
−
119
x
2
+
49
x
−
6
)
=
0
is
3
5
,
find the remaining real roots
(i)
(
1
5
,
0
)
(ii)
(
2
9
,
1
2
)
(iii)
(
1
,
4
9
)
(iv)
(
3
7
,
2
11
)
(v)
(
1
,
2
7
)
Question
14
14.
If one of the roots of the cubic equation
(
x
3
−
5
x
2
−
28
x
+
32
)
=
0
is
8
,
find the remaining real roots
(i)
(
9
,
(
−
3
)
)
(ii)
(
6
,
(
−
7
)
)
(iii)
(
(
−
4
)
,
1
)
(iv)
(
10
,
(
−
1
)
)
(v)
(
7
,
(
−
5
)
)
Question
15
15.
If
α
=
5
9
,
β
=
3
2
,
γ
=
6
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
109
42
)
(ii)
(
−
367
126
)
(iii)
109
42
(iv)
367
126
(v)
(
−
5
7
)
Question
16
16.
If
α
=
7
2
,
β
=
9
2
,
γ
=
7
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
(
−
413
12
)
(ii)
413
12
(iii)
31
3
(iv)
(
−
147
4
)
(v)
147
4
Question
17
17.
If
α
=
1
4
,
β
=
3
4
,
γ
=
2
5
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
7
5
)
(ii)
7
5
(iii)
47
80
(iv)
(
−
47
80
)
(v)
(
−
3
40
)
Question
18
18.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
−
6
x
−
6
,
find the value of
a
(i)
(-4)
(ii)
(-2)
(iii)
0
(iv)
(-1)
(v)
1
Assignment Key
1) (ii)
2) (ii)
3) (iii)
4) (iii)
5) (iv)
6) (iv)
7) (iv)
8) (iv)
9) (iii)
10) (iii)
11) (iii)
12) (iv)
13) (ii)
14) (iii)
15) (ii)
16) (ii)
17) (v)
18) (iv)
