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
8
x
4
+
32
x
3
−
112
x
2
+
k
x
+
360
is exactly divisible by
(
x
+
5
)
(i)
-286
(ii)
-290
(iii)
-287
(iv)
-288
(v)
-289
Question
2
2.
If
2
and
-2
are the zeros of the polynomial
f
(
x
)
=
8
x
4
−
8
x
3
−
38
x
2
+
b
x
+
a
, find the value of
a
and
b
(i)
31
,
23
(ii)
24
,
32
(iii)
24
,
33
(iv)
25
,
32
(v)
33
,
25
Question
3
3.
Find the value of
a
and
b
such that
a
x
4
+
b
x
3
−
72
x
2
−
170
x
−
100
is exactly divisible by
(
x
2
−
3
x
−
10
)
(i)
4
,
2
(ii)
3
,
5
(iii)
1
,
3
(iv)
4
,
3
(v)
5
,
2
Question
4
4.
If
5
3
is the zero of the polynomial
f
(
x
)
=
3
x
2
+
10
x
+
k
,
find
k
(i)
-25
(ii)
-23
(iii)
-28
(iv)
-24
(v)
-26
Question
5
5.
If the polynomial
f
(
x
)
=
9
x
2
+
15
x
+
k
is exactly divisible by
(
3
x
+
2
)
,
find
k
(i)
8
(ii)
6
(iii)
5
(iv)
7
(v)
4
Question
6
6.
If the polynomials
a
x
2
+
x
−
31
and
−
2
x
2
+
a
x
−
11
leave the same remainder when divided by
(
x
−
2
)
,
find the value of
a
(i)
5
(ii)
2
(iii)
8
(iv)
6
(v)
4
Question
7
7.
Which of the following are true?
a)
Zero of a polynomial and zero polynomial are synonymous
b)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
c)
A linear polynomial in one variable has only one root
d)
A polynomial of degree n has atmost n zeros
e)
Zero of a polynomial and root of the polynomial are synonymous
f)
If (x + a) is a factor of f(x), then f(a) = 0
g)
If (x - a) is a factor of f(x), then f(a) = 0
(i)
{a,e,g}
(ii)
{a,b}
(iii)
{a,f,d}
(iv)
{f,c}
(v)
{b,c,d,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 + d + e = 0
b)
a + b + c = 0
c)
a + b + c = d + e
d)
d + e = 0
e)
a + c + e = 0
f)
b + d = 0
(i)
{b,a}
(ii)
{c,a,e}
(iii)
{d,b,f}
(iv)
{a,e,f}
(v)
{c,e}
Question
9
9.
Find the value of
k
such that
8
x
3
−
12
x
2
−
32
x
+
k
is exactly divisible by
(
2
x
−
4
)
(i)
48
(ii)
45
(iii)
49
(iv)
51
(v)
47
Question
10
10.
If
3
and
-1
are the zeros of the polynomial
f
(
x
)
=
4
x
4
+
a
x
2
+
b
x
, find the value of
a
and
b
(i)
-28
,
-24
(ii)
-28
,
-23
(iii)
-27
,
-24
(iv)
-25
,
-29
(v)
-23
,
-27
Question
11
11.
Find the value of
a
and
b
such that
2
x
4
+
a
x
3
+
b
x
2
−
42
x
−
36
is exactly divisible by
(
x
2
+
x
−
6
)
(i)
11
,
2
(ii)
3
,
11
(iii)
10
,
2
(iv)
1
,
9
(v)
10
,
3
Question
12
12.
If
-2
is the zero of the polynomial
f
(
x
)
=
k
x
2
+
27
x
+
30
,
find
k
(i)
7
(ii)
9
(iii)
6
(iv)
3
(v)
5
Question
13
13.
If the polynomial
f
(
x
)
=
k
x
2
−
14
x
+
6
is exactly divisible by
(
2
x
−
6
)
,
find
k
(i)
3
(ii)
4
(iii)
1
(iv)
5
(v)
7
Question
14
14.
If the polynomials
−
2
x
2
+
a
x
+
22
and
a
x
2
−
4
x
+
34
leave the same remainder when divided by
(
x
−
2
)
,
find the value of
a
(i)
(-8)
(ii)
(-7)
(iii)
(-3)
(iv)
(-5)
(v)
(-6)
Assignment Key
1) (iv)
2) (ii)
3) (i)
4) (i)
5) (ii)
6) (i)
7) (v)
8) (iv)
9) (i)
10) (i)
11) (iii)
12) (iii)
13) (ii)
14) (v)
