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
4
x
3
+
k
x
−
216
is exactly divisible by
(
x
−
6
)
(i)
-109
(ii)
-108
(iii)
-111
(iv)
-105
(v)
-107
Question
2
2.
If
5
and
(
-1
2
)
are the zeros of the polynomial
f
(
x
)
=
4
x
4
+
a
x
3
+
b
x
2
−
38
x
−
10
, find the value of
a
and
b
(i)
-10
,
-41
(ii)
-10
,
-42
(iii)
-9
,
-42
(iv)
-41
,
-9
(v)
-43
,
-11
Question
3
3.
Find the value of
a
and
b
such that
a
x
4
−
4
x
3
−
44
x
2
+
16
x
+
b
is exactly divisible by
(
4
x
2
+
2
x
−
12
)
(i)
8
,
48
(ii)
8
,
49
(iii)
49
,
9
(iv)
47
,
7
(v)
9
,
48
Question
4
4.
If
2
is the zero of the polynomial
f
(
x
)
=
3
x
2
+
6
x
+
k
,
find
k
(i)
-27
(ii)
-22
(iii)
-24
(iv)
-23
(v)
-25
Question
5
5.
If the polynomial
f
(
x
)
=
2
x
2
−
14
x
+
k
is exactly divisible by
(
x
−
6
)
,
find
k
(i)
11
(ii)
9
(iii)
14
(iv)
12
(v)
13
Question
6
6.
If the polynomials
a
x
2
−
4
x
−
30
and
−
3
x
2
+
a
x
+
14
leave the same remainder when divided by
(
x
+
2
)
,
find the value of
a
(i)
3
(ii)
6
(iii)
2
(iv)
4
(v)
5
Question
7
7.
Which of the following are true?
a)
A polynomial of degree n has atmost n zeros
b)
If (x - a) is a factor of f(x), then f(a) = 0
c)
A linear polynomial in one variable has only one root
d)
Zero of a polynomial and zero polynomial are synonymous
e)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
f)
Zero of a polynomial and root of the polynomial are synonymous
g)
If (x + a) is a factor of f(x), then f(a) = 0
(i)
{d,e,f}
(ii)
{d,g,c}
(iii)
{a,b,c,e,f}
(iv)
{g,b}
(v)
{d,a}
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)
d + e = 0
b)
a + c + e = 0
c)
b + d = 0
d)
a + b + c = 0
e)
a + b + c = d + e
f)
a + b + c + d + e = 0
(i)
{d,b,c}
(ii)
{e,a,f}
(iii)
{b,c,f}
(iv)
{d,c}
(v)
{a,b}
Question
9
9.
Find the value of
k
such that
x
3
+
k
x
2
−
x
−
5
is exactly divisible by
(
x
−
1
)
(i)
2
(ii)
6
(iii)
7
(iv)
5
(v)
4
Question
10
10.
If
1
and
-1
are the zeros of the polynomial
f
(
x
)
=
2
x
4
+
a
x
3
−
10
x
2
+
b
x
+
8
, find the value of
a
and
b
(i)
6
,
-5
(ii)
6
,
-6
(iii)
-5
,
7
(iv)
-7
,
5
(v)
7
,
-6
Question
11
11.
Find the value of
a
and
b
such that
b
x
4
+
a
x
3
−
19
x
2
+
20
x
is exactly divisible by
(
x
2
+
3
x
−
4
)
(i)
-1
,
1
(ii)
0
,
-3
(iii)
-2
,
2
(iv)
-2
,
1
(v)
2
,
-1
Question
12
12.
If
(
-5
3
)
is the zero of the polynomial
f
(
x
)
=
6
x
2
+
16
x
+
k
,
find
k
(i)
9
(ii)
8
(iii)
11
(iv)
13
(v)
10
Question
13
13.
If the polynomial
f
(
x
)
=
k
x
2
−
9
x
−
5
is exactly divisible by
(
2
x
+
1
)
,
find
k
(i)
2
(ii)
3
(iii)
4
(iv)
1
(v)
-1
Question
14
14.
If the polynomials
−
5
x
2
+
a
x
+
29
and
a
x
2
+
2
x
−
58
leave the same remainder when divided by
(
x
−
3
)
,
find the value of
a
(i)
3
(ii)
6
(iii)
7
(iv)
5
(v)
8
Assignment Key
1) (ii)
2) (ii)
3) (i)
4) (iii)
5) (iv)
6) (iv)
7) (iii)
8) (iii)
9) (iv)
10) (ii)
11) (iv)
12) (v)
13) (i)
14) (ii)
