EduSahara™ Assignment
Name : Zeros of a Polynomial
Chapter : Polynomials and Factorisation
Grade : SSC Grade IX
License : Non Commercial Use
Question
1
1.
Find the value of
k
such that
k
x
4
−
4
x
3
−
96
x
2
+
176
x
−
64
is exactly divisible by
(
2
x
−
4
)
(i)
9
(ii)
8
(iii)
6
(iv)
11
(v)
7
Question
2
2.
If
2
and
-1
are the zeros of the polynomial
f
(
x
)
=
b
x
4
+
9
x
3
+
a
x
−
30
, find the value of
a
and
b
(i)
3
,
-36
(ii)
-37
,
3
(iii)
-37
,
2
(iv)
-36
,
2
(v)
1
,
-38
Question
3
3.
Find the value of
a
and
b
such that
4
x
4
−
34
x
3
+
36
x
2
+
b
x
+
a
is exactly divisible by
(
4
x
2
+
6
x
−
4
)
(i)
189
,
-101
(ii)
-99
,
190
(iii)
-100
,
190
(iv)
-100
,
191
(v)
191
,
-99
Question
4
4.
If
-4
is the zero of the polynomial
f
(
x
)
=
k
x
2
+
9
x
+
4
,
find
k
(i)
-1
(ii)
2
(iii)
1
(iv)
3
(v)
4
Question
5
5.
If the polynomial
f
(
x
)
=
2
x
2
+
4
x
+
k
is exactly divisible by
(
x
+
4
)
,
find
k
(i)
-13
(ii)
-16
(iii)
-15
(iv)
-18
(v)
-17
Question
6
6.
If the polynomials
3
x
2
+
a
x
−
9
and
a
x
2
−
5
x
+
51
leave the same remainder when divided by
(
x
−
3
)
,
find the value of
a
(i)
(-2)
(ii)
(-3)
(iii)
(-4)
(iv)
(-1)
(v)
(-6)
Question
7
7.
Which of the following are true?
a)
A polynomial of degree n has atmost n zeros
b)
A linear polynomial in one variable has only one root
c)
Zero of a polynomial and root of the polynomial are synonymous
d)
Zero of a polynomial and zero polynomial are synonymous
e)
If (x - a) is a factor of f(x), then f(a) = 0
f)
If (x + a) is a factor of f(x), then f(a) = 0
g)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
(i)
{f,b}
(ii)
{d,a}
(iii)
{d,e,g}
(iv)
{d,f,c}
(v)
{a,b,c,e,g}
Question
8
8.
If
(
x
2
−
1
)
is a factor of
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
,
which of the following are true ?
a)
a + b + c = 0
b)
b + d = 0
c)
d + e = 0
d)
a + c + e = 0
e)
a + b + c = d + e
f)
a + b + c + d + e = 0
(i)
{c,d}
(ii)
{a,b}
(iii)
{c,b,d}
(iv)
{b,d,f}
(v)
{e,a,f}
Question
9
9.
Find the value of
k
such that
k
x
3
+
20
x
2
+
24
x
is exactly divisible by
(
x
+
3
)
(i)
5
(ii)
3
(iii)
2
(iv)
4
(v)
6
Question
10
10.
If
2
and
(
-5
2
)
are the zeros of the polynomial
f
(
x
)
=
8
x
4
+
b
x
3
+
a
x
2
−
220
x
−
400
, find the value of
a
and
b
(i)
66
,
57
(ii)
67
,
56
(iii)
57
,
67
(iv)
66
,
56
(v)
55
,
65
Question
11
11.
Find the value of
a
and
b
such that
2
x
4
−
2
x
3
−
42
x
2
+
b
x
+
a
is exactly divisible by
(
x
2
−
x
−
20
)
(i)
41
,
2
(ii)
3
,
41
(iii)
40
,
3
(iv)
1
,
39
(v)
40
,
2
Question
12
12.
If
1
is the zero of the polynomial
f
(
x
)
=
k
x
2
−
12
x
+
3
,
find
k
(i)
6
(ii)
12
(iii)
8
(iv)
10
(v)
9
Question
13
13.
If the polynomial
f
(
x
)
=
6
x
2
+
k
x
−
4
is exactly divisible by
(
2
x
−
1
)
,
find
k
(i)
6
(ii)
3
(iii)
4
(iv)
8
(v)
5
Question
14
14.
If the polynomials
5
x
2
+
a
x
−
13
and
a
x
2
−
2
x
+
9
leave the same remainder when divided by
(
x
−
2
)
,
find the value of
a
(i)
4
(ii)
2
(iii)
(-1)
(iv)
0
(v)
1
Assignment Key
1) (ii)
2) (iii)
3) (iii)
4) (ii)
5) (ii)
6) (ii)
7) (v)
8) (iv)
9) (iv)
10) (iv)
11) (v)
12) (v)
13) (v)
14) (v)
