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
(
200
x
3
−
825
x
2
+
1123
x
−
504
)
=
0
,
find
α + β + γ
(i)
(
−
1123
200
)
(ii)
33
8
(iii)
(
−
63
25
)
(iv)
(
−
33
8
)
(v)
1123
200
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
180
x
3
−
221
x
2
+
72
x
−
7
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
7
180
)
(ii)
221
180
(iii)
7
180
(iv)
(
−
2
5
)
(v)
2
5
Question
3
3.
If
α, β, γ
are the roots of the cubic equation
(
567
x
3
−
810
x
2
+
341
x
−
42
)
=
0
,
find
αβγ
(i)
341
567
(ii)
10
7
(iii)
2
27
(iv)
(
−
341
567
)
(v)
(
−
2
27
)
Question
4
4.
If one of the roots of the cubic equation
(
72
x
3
−
159
x
2
+
116
x
−
28
)
=
0
is
2
3
,
find the remaining real roots
(i)
(
2
3
,
7
8
)
(ii)
(
0
,
0
)
(iii)
(
4
3
,
4
3
)
(iv)
(
2
,
2
)
(v)
(
2
5
,
2
5
)
Question
5
5.
If one of the roots of the cubic equation
(
x
3
+
4
x
2
−
17
x
−
60
)
=
0
is
4
,
find the remaining real roots
(i)
(
6
,
(
−
2
)
)
(ii)
(
(
−
5
)
,
(
−
3
)
)
(iii)
(
5
,
(
−
4
)
)
(iv)
(
3
,
(
−
6
)
)
(v)
(
2
,
(
−
8
)
)
Question
6
6.
If
α
=
4
7
,
β
=
2
7
,
γ
=
3
2
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
12
49
)
(ii)
33
14
(iii)
(
−
71
49
)
(iv)
71
49
(v)
(
−
33
14
)
Question
7
7.
If
α
=
9
4
,
β
=
8
9
,
γ
=
1
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
2
7
(ii)
(
−
617
252
)
(iii)
827
252
(iv)
617
252
(v)
(
−
2
7
)
Question
8
8.
If
α
=
1
6
,
β
=
7
5
,
γ
=
4
9
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
14
135
)
(ii)
251
270
(iii)
181
90
(iv)
14
135
(v)
(
−
251
270
)
Question
9
9.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
−
6
x
−
24
,
find the value of
a
(i)
(-5)
(ii)
(-7)
(iii)
(-1)
(iv)
(-3)
(v)
(-4)
Question
10
10.
If
α, β, γ
are the roots of the cubic equation
(
243
x
3
−
756
x
2
+
705
x
−
200
)
=
0
,
find
α + β + γ
(i)
(
−
200
243
)
(ii)
(
−
28
9
)
(iii)
28
9
(iv)
200
243
(v)
(
−
235
81
)
Question
11
11.
If
α, β, γ
are the roots of the cubic equation
(
168
x
3
−
653
x
2
+
690
x
−
189
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
653
168
)
(ii)
653
168
(iii)
115
28
(iv)
9
8
(v)
(
−
115
28
)
Question
12
12.
If
α, β, γ
are the roots of the cubic equation
(
392
x
3
−
1127
x
2
+
1046
x
−
315
)
=
0
,
find
αβγ
(i)
(
−
23
8
)
(ii)
(
−
45
56
)
(iii)
45
56
(iv)
23
8
(v)
(
−
523
196
)
Question
13
13.
If one of the roots of the cubic equation
(
90
x
3
−
629
x
2
+
1136
x
−
576
)
=
0
is
9
2
,
find the remaining real roots
(i)
(
7
2
,
2
3
)
(ii)
(
17
4
,
8
11
)
(iii)
(
11
2
,
10
9
)
(iv)
(
8
9
,
8
5
)
(v)
(
5
,
8
7
)
Question
14
14.
If one of the roots of the cubic equation
(
x
3
−
9
x
2
+
23
x
−
15
)
=
0
is
5
,
find the remaining real roots
(i)
(
3
,
1
)
(ii)
(
4
,
2
)
(iii)
(
8
,
6
)
(iv)
(
6
,
4
)
Question
15
15.
If
α
=
7
8
,
β
=
5
3
,
γ
=
9
8
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
829
192
)
(ii)
(
−
11
3
)
(iii)
105
64
(iv)
(
−
105
64
)
(v)
11
3
Question
16
16.
If
α
=
1
3
,
β
=
1
7
,
γ
=
7
2
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
167
42
(ii)
1
6
(iii)
12
7
(iv)
(
−
12
7
)
(v)
(
−
1
6
)
Question
17
17.
If
α
=
5
3
,
β
=
5
9
,
γ
=
8
5
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
40
27
)
(ii)
172
45
(iii)
40
27
(iv)
121
27
(v)
(
−
121
27
)
Question
18
18.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
+
9
x
+
9
,
find the value of
a
(i)
(-4)
(ii)
0
(iii)
(-1)
(iv)
2
(v)
(-2)
Assignment Key
1) (ii)
2) (v)
3) (iii)
4) (i)
5) (ii)
6) (v)
7) (iv)
8) (i)
9) (v)
10) (iii)
11) (iii)
12) (iii)
13) (iv)
14) (i)
15) (ii)
16) (iii)
17) (i)
18) (iii)
