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
(
90
x
3
−
347
x
2
+
408
x
−
135
)
=
0
,
find
α + β + γ
(i)
3
2
(ii)
68
15
(iii)
347
90
(iv)
(
−
3
2
)
(v)
(
−
68
15
)
Question
2
2.
If
α, β, γ
are the roots of the cubic equation
(
42
x
3
−
307
x
2
+
688
x
−
448
)
=
0
,
find
αβ + βγ + γα
(i)
(
−
32
3
)
(ii)
307
42
(iii)
(
−
307
42
)
(iv)
344
21
(v)
(
−
344
21
)
Question
3
3.
If
α, β, γ
are the roots of the cubic equation
(
224
x
3
−
324
x
2
+
147
x
−
20
)
=
0
,
find
αβγ
(i)
21
32
(ii)
(
−
5
56
)
(iii)
(
−
21
32
)
(iv)
81
56
(v)
5
56
Question
4
4.
If one of the roots of the cubic equation
(
30
x
3
−
191
x
2
+
386
x
−
240
)
=
0
is
5
2
,
find the remaining real roots
(i)
(
3
,
4
)
(ii)
(
7
2
,
10
3
)
(iii)
(
3
2
,
2
)
(iv)
(
8
3
,
6
5
)
(v)
(
9
4
,
12
5
)
Question
5
5.
If one of the roots of the cubic equation
(
x
3
−
2
x
2
−
15
x
)
=
0
is
(
−
3
)
,
find the remaining real roots
(i)
(
(
−
6
)
,
2
)
(ii)
(
5
,
0
)
(iii)
(
(
−
4
)
,
4
)
(iv)
(
(
−
2
)
,
6
)
(v)
(
(
−
1
)
,
8
)
Question
6
6.
If
α
=
5
6
,
β
=
8
9
,
γ
=
7
5
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
(
−
281
90
)
(ii)
(
−
851
270
)
(iii)
851
270
(iv)
28
27
(v)
281
90
Question
7
7.
If
α
=
8
7
,
β
=
9
2
,
γ
=
9
4
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
(
−
999
56
)
(ii)
221
28
(iii)
81
7
(iv)
999
56
(v)
(
−
81
7
)
Question
8
8.
If
α
=
1
9
,
β
=
2
5
,
γ
=
6
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
152
315
(ii)
4
105
(iii)
(
−
431
315
)
(iv)
(
−
4
105
)
(v)
431
315
Question
9
9.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
−
6
x
−
6
,
find the value of
a
(i)
(-2)
(ii)
0
(iii)
1
(iv)
(-4)
(v)
(-1)
Question
10
10.
If
α, β, γ
are the roots of the cubic equation
(
112
x
3
−
474
x
2
+
569
x
−
210
)
=
0
,
find
α + β + γ
(i)
237
56
(ii)
(
−
237
56
)
(iii)
(
−
569
112
)
(iv)
15
8
(v)
569
112
Question
11
11.
If
α, β, γ
are the roots of the cubic equation
(
189
x
3
−
363
x
2
+
196
x
−
32
)
=
0
,
find
αβ + βγ + γα
(i)
121
63
(ii)
(
−
32
189
)
(iii)
(
−
121
63
)
(iv)
28
27
(v)
(
−
28
27
)
Question
12
12.
If
α, β, γ
are the roots of the cubic equation
(
288
x
3
−
788
x
2
+
525
x
−
49
)
=
0
,
find
αβγ
(i)
(
−
175
96
)
(ii)
(
−
49
288
)
(iii)
49
288
(iv)
197
72
(v)
(
−
197
72
)
Question
13
13.
If one of the roots of the cubic equation
(
175
x
3
−
605
x
2
+
684
x
−
252
)
=
0
is
6
7
,
find the remaining real roots
(i)
(
8
7
,
9
5
)
(ii)
(
2
3
,
9
7
)
(iii)
(
4
7
,
1
)
(iv)
(
7
5
,
6
5
)
(v)
(
6
5
,
5
3
)
Question
14
14.
If one of the roots of the cubic equation
(
x
3
+
14
x
2
+
55
x
+
42
)
=
0
is
(
−
7
)
,
find the remaining real roots
(i)
(
(
−
10
)
,
(
−
3
)
)
(ii)
(
(
−
6
)
,
0
)
(iii)
(
(
−
8
)
,
(
−
2
)
)
(iv)
(
(
−
4
)
,
1
)
(v)
(
(
−
1
)
,
(
−
6
)
)
Question
15
15.
If
α
=
8
9
,
β
=
3
4
,
γ
=
4
5
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
b
a
(i)
89
45
(ii)
8
15
(iii)
(
−
439
180
)
(iv)
(
−
89
45
)
(v)
439
180
Question
16
16.
If
α
=
2
3
,
β
=
5
6
,
γ
=
9
7
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
(
−
39
14
)
(ii)
(
−
5
7
)
(iii)
313
126
(iv)
39
14
(v)
5
7
Question
17
17.
If
α
=
1
6
,
β
=
3
4
,
γ
=
1
3
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
d
a
(i)
(
−
31
72
)
(ii)
1
24
(iii)
31
72
(iv)
(
−
5
4
)
(v)
(
−
1
24
)
Assignment Key
1) (iii)
2) (iv)
3) (v)
4) (iv)
5) (ii)
6) (i)
7) (iv)
8) (iv)
9) (v)
10) (i)
11) (iv)
12) (iii)
13) (iv)
14) (v)
15) (iii)
16) (iii)
17) (v)
