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
+
x
2
−
20
x
is exactly divisible by
(
x
+
5
)
(i)
2
(ii)
-2
(iii)
0
(iv)
1
(v)
3
Question
2
2.
If
1
2
and
-4
are the zeros of the polynomial
f
(
x
)
=
a
x
4
−
7
x
3
+
b
x
2
+
98
x
−
40
, find the value of
a
and
b
(i)
-32
,
3
(ii)
-34
,
1
(iii)
3
,
-33
(iv)
2
,
-32
(v)
2
,
-33
Question
3
3.
Find the value of
a
and
b
such that
b
x
4
+
4
x
3
−
20
x
2
+
a
x
is exactly divisible by
(
x
2
+
2
x
−
3
)
(i)
12
,
5
(ii)
12
,
4
(iii)
5
,
13
(iv)
13
,
4
(v)
3
,
11
Question
4
4.
If
-1
is the zero of the polynomial
f
(
x
)
=
k
x
2
−
3
x
−
4
,
find
k
(i)
4
(ii)
1
(iii)
0
(iv)
-2
(v)
2
Question
5
5.
If the polynomial
f
(
x
)
=
2
x
2
+
k
x
+
12
is exactly divisible by
(
x
−
4
)
,
find
k
(i)
-12
(ii)
-8
(iii)
-10
(iv)
-13
(v)
-11
Question
6
6.
If the polynomials
a
x
2
−
6
x
−
48
and
6
x
2
+
a
x
−
48
leave the same remainder when divided by
(
x
+
3
)
,
find the value of
a
(i)
5
(ii)
1
(iii)
3
(iv)
4
(v)
2
Question
7
7.
Which of the following are true?
a)
Zero of a polynomial and zero polynomial are synonymous
b)
A linear polynomial in one variable has only one root
c)
If (x - a) is a factor of f(x), then f(a) = 0
d)
Zero of a polynomial and root of the polynomial are synonymous
e)
If (x + a) is a factor of f(x), then f(a) = 0
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)
{a,f,g}
(ii)
{b,c,d,f,g}
(iii)
{e,c}
(iv)
{a,b}
(v)
{a,e,d}
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)
b + d = 0
c)
a + b + c = 0
d)
a + b + c = d + e
e)
a + c + e = 0
f)
d + e = 0
(i)
{d,b}
(ii)
{a,b,e}
(iii)
{d,a,b}
(iv)
{f,c,e}
(v)
{c,a}
Question
9
9.
Find the value of
k
such that
4
x
3
+
k
x
2
−
44
x
−
24
is exactly divisible by
(
2
x
+
2
)
(i)
-13
(ii)
-17
(iii)
-18
(iv)
-15
(v)
-16
Question
10
10.
If
4
and
(
-1
2
)
are the zeros of the polynomial
f
(
x
)
=
4
x
4
+
a
x
3
−
48
x
2
−
88
x
+
b
, find the value of
a
and
b
(i)
-31
,
3
(ii)
3
,
-32
(iii)
2
,
-32
(iv)
2
,
-31
(v)
-33
,
1
Question
11
11.
Find the value of
a
and
b
such that
b
x
4
+
a
x
2
+
225
is exactly divisible by
(
2
x
2
−
x
−
15
)
(i)
3
,
-62
(ii)
5
,
-60
(iii)
-61
,
5
(iv)
-60
,
4
(v)
-61
,
4
Question
12
12.
If
-5
is the zero of the polynomial
f
(
x
)
=
2
x
2
+
k
x
+
20
,
find
k
(i)
15
(ii)
13
(iii)
17
(iv)
12
(v)
14
Question
13
13.
If the polynomial
f
(
x
)
=
k
x
2
−
x
−
6
is exactly divisible by
(
x
−
2
)
,
find
k
(i)
3
(ii)
0
(iii)
2
(iv)
1
(v)
4
Question
14
14.
If the polynomials
a
x
2
−
5
x
+
24
and
3
x
2
+
a
x
−
30
leave the same remainder when divided by
(
x
−
3
)
,
find the value of
a
(i)
(-3)
(ii)
(-2)
(iii)
(-4)
(iv)
(-1)
(v)
0
Assignment Key
1) (iv)
2) (v)
3) (ii)
4) (ii)
5) (v)
6) (iii)
7) (ii)
8) (ii)
9) (v)
10) (iii)
11) (v)
12) (v)
13) (iii)
14) (ii)
