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
3
−
4
x
2
−
16
x
+
16
is exactly divisible by
(
2
x
−
2
)
(i)
1
(ii)
4
(iii)
5
(iv)
3
(v)
7
Question
2
2.
If
3
and
-1
are the zeros of the polynomial
f
(
x
)
=
b
x
4
+
a
x
3
+
17
x
2
+
26
x
−
15
, find the value of
a
and
b
(i)
-20
,
4
(ii)
3
,
-21
(iii)
5
,
-19
(iv)
-20
,
5
(v)
-19
,
4
Question
3
3.
Find the value of
a
and
b
such that
2
x
4
+
a
x
3
+
x
2
+
b
x
+
9
is exactly divisible by
(
x
2
+
2
x
−
3
)
(i)
-20
,
10
(ii)
-22
,
8
(iii)
9
,
-21
(iv)
9
,
-20
(v)
10
,
-21
Question
4
4.
If
4
3
is the zero of the polynomial
f
(
x
)
=
k
x
2
−
7
x
+
4
,
find
k
(i)
6
(ii)
4
(iii)
0
(iv)
3
(v)
2
Question
5
5.
If the polynomial
f
(
x
)
=
x
2
+
k
x
−
24
is exactly divisible by
(
x
−
4
)
,
find
k
(i)
2
(ii)
1
(iii)
5
(iv)
3
(v)
0
Question
6
6.
If the polynomials
a
x
2
−
3
x
−
25
and
6
x
2
+
a
x
−
46
leave the same remainder when divided by
(
x
+
3
)
,
find the value of
a
(i)
5
(ii)
1
(iii)
3
(iv)
(-1)
(v)
2
Question
7
7.
Which of the following are true?
a)
Zero of a polynomial and zero polynomial are synonymous
b)
If (x - a) is a factor of f(x), then f(a) = 0
c)
If (x + a) is a factor of f(x), then f(a) = 0
d)
A linear polynomial in one variable has only one root
e)
Zero of a polynomial and root of the polynomial are synonymous
f)
A polynomial of degree n has atmost n zeros
g)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
(i)
{b,d,e,f,g}
(ii)
{a,b}
(iii)
{c,d}
(iv)
{a,f,g}
(v)
{a,c,e}
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)
b + d = 0
b)
a + b + c = 0
c)
d + e = 0
d)
a + c + e = 0
e)
a + b + c + d + e = 0
f)
a + b + c = d + e
(i)
{f,b,e}
(ii)
{a,d,e}
(iii)
{c,d}
(iv)
{b,a}
(v)
{c,a,d}
Question
9
9.
Find the value of
k
such that
8
x
3
+
8
x
2
−
2
x
+
k
is exactly divisible by
(
2
x
+
1
)
(i)
0
(ii)
-5
(iii)
-3
(iv)
-2
(v)
-1
Question
10
10.
If
4
and
-1
are the zeros of the polynomial
f
(
x
)
=
4
x
4
−
16
x
3
+
a
x
2
+
b
x
, find the value of
a
and
b
(i)
-3
,
16
(ii)
-4
,
16
(iii)
17
,
-3
(iv)
15
,
-5
(v)
-4
,
17
Question
11
11.
Find the value of
a
and
b
such that
4
x
4
−
12
x
3
+
b
x
2
+
a
x
+
120
is exactly divisible by
(
2
x
2
+
2
x
−
12
)
(i)
76
,
-59
(ii)
77
,
-60
(iii)
76
,
-60
(iv)
-59
,
77
(v)
-61
,
75
Question
12
12.
If
2
is the zero of the polynomial
f
(
x
)
=
4
x
2
−
2
x
+
k
,
find
k
(i)
-13
(ii)
-10
(iii)
-12
(iv)
-11
(v)
-15
Question
13
13.
If the polynomial
f
(
x
)
=
k
x
2
+
6
x
−
12
is exactly divisible by
(
2
x
−
2
)
,
find
k
(i)
8
(ii)
6
(iii)
5
(iv)
4
(v)
7
Question
14
14.
If the polynomials
−
x
2
+
a
x
+
25
and
a
x
2
−
6
x
−
38
leave the same remainder when divided by
(
x
+
3
)
,
find the value of
a
(i)
3
(ii)
0
(iii)
2
(iv)
4
(v)
5
Assignment Key
1) (ii)
2) (i)
3) (iii)
4) (iv)
5) (i)
6) (v)
7) (i)
8) (ii)
9) (iv)
10) (ii)
11) (iii)
12) (iii)
13) (ii)
14) (i)
