EduSahara™ Assignment
Name : Zeroes of a Quadratic Polynomial
Chapter : Polynomials
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
If (x - a) is a factor of f(x), then f(a) = 0
b)
Zero of a polynomial and root of the polynomial are synonymous
c)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
d)
Zero of a polynomial and zero polynomial are synonymous
e)
A polynomial of degree n has atmost n zeros
f)
A linear polynomial in one variable has only one root
g)
If (x + a) is a factor of f(x), then f(a) = 0
(i)
{d,e,f}
(ii)
{a,b,c,e,f}
(iii)
{d,g,c}
(iv)
{g,b}
(v)
{d,a}
Question
2
2.
Which of the following are true?
a)
Every polynomial is a binomial
b)
A binomial may have degree 3
c)
Degree of zero polynomial is zero
d)
A binomial has two and only two terms
e)
π
r
2
is a monomial
(i)
{a,c,e}
(ii)
{b,d,e}
(iii)
{a,b}
(iv)
{c,d}
(v)
{a,b,d}
Question
3
3.
If
2
and
-1
are the zeros of the polynomial
f
(
x
)
=
2
x
4
−
4
x
3
+
b
x
2
+
a
x
, find the value of
a
and
b
(i)
-1
,
5
(ii)
-3
,
3
(iii)
4
,
-1
(iv)
5
,
-2
(v)
4
,
-2
Question
4
4.
If
2
is the zero of the polynomial
f
(
x
)
=
x
2
+
4
x
+
k
,
find
k
(i)
-13
(ii)
-14
(iii)
-12
(iv)
-9
(v)
-11
Question
5
5.
Find the quadratic equation with roots
(
9
4
,
9
4
)
(i)
(
16
x
2
−
72
x
+
81
)
=
0
(ii)
(
16
x
2
−
64
x
+
63
)
=
0
(iii)
(
8
x
2
−
54
x
+
81
)
=
0
(iv)
(
16
x
2
−
80
x
+
99
)
=
0
(v)
(
8
x
2
−
30
x
+
27
)
=
0
Question
6
6.
Find the quadratic equation with roots
(
6
7
,
1
4
)
(i)
(
42
x
2
−
43
x
+
6
)
=
0
(ii)
(
28
x
2
−
45
x
+
18
)
=
0
(iii)
(
20
x
2
−
29
x
+
6
)
=
0
(iv)
(
28
x
2
−
31
x
+
6
)
=
0
(v)
(
28
x
2
−
23
x
+
4
)
=
0
Question
7
7.
Find the quadratic equation with roots
(
5
,
5
)
(i)
(
x
2
−
10
x
+
25
)
=
0
(ii)
(
x
2
−
9
x
+
20
)
=
0
(iii)
(
x
2
−
13
x
+
40
)
=
0
(iv)
(
x
2
−
8
x
+
15
)
=
0
(v)
(
x
2
−
11
x
+
30
)
=
0
Question
8
8.
Find the quadratic equation with roots
(
5
,
-6
)
(i)
(
x
2
+
4
x
−
12
)
=
0
(ii)
(
x
2
−
2
x
−
15
)
=
0
(iii)
(
x
2
+
x
−
30
)
=
0
(iv)
(
x
2
−
25
)
=
0
(v)
(
x
2
+
2
x
−
24
)
=
0
Question
9
9.
The sum of the roots of the quadratic equation
(
x
2
−
12
x
+
36
)
=
0
is
(i)
11
(ii)
15
(iii)
9
(iv)
12
(v)
13
Question
10
10.
The sum of the roots of the quadratic equation
(
x
2
+
15
x
+
54
)
=
0
is
(i)
-14
(ii)
-15
(iii)
-17
(iv)
-12
(v)
-16
Question
11
11.
The sum of the roots of the quadratic equation
(
x
2
−
16
x
+
64
)
=
0
is
(i)
18
(ii)
14
(iii)
17
(iv)
16
(v)
15
Question
12
12.
The sum of the roots of the quadratic equation
(
−
45
x
2
−
72
x
−
27
)
=
0
is
(i)
(
-10
7
)
(ii)
-2
(iii)
(
-8
5
)
(iv)
(
-6
5
)
Question
13
13.
The product of the roots of the quadratic equation
(
x
2
+
16
x
+
64
)
=
0
is
(i)
62
(ii)
65
(iii)
67
(iv)
63
(v)
64
Question
14
14.
The product of the roots of the quadratic equation
(
x
2
−
3
x
+
2
)
=
0
is
(i)
0
(ii)
2
(iii)
3
(iv)
1
(v)
4
Question
15
15.
The product of the roots of the quadratic equation
(
49
x
2
−
42
x
+
9
)
=
0
is
(i)
3
17
(ii)
1
7
(iii)
11
49
(iv)
9
47
(v)
9
49
Question
16
16.
The product of the roots of the quadratic equation
(
−
35
x
2
−
47
x
−
8
)
=
0
is
(i)
8
33
(ii)
8
35
(iii)
2
7
(iv)
6
35
(v)
8
37
Question
17
17.
Find the quadratic equation, the sum of whose roots is
-16
and product is
64
(i)
(
x
2
+
13
x
+
64
)
=
0
(ii)
(
x
2
+
16
x
+
64
)
=
0
(iii)
(
16
x
+
64
)
=
0
(iv)
(
2
x
2
+
16
x
+
64
)
=
0
(v)
(
x
2
+
19
x
+
64
)
=
0
Question
18
18.
Find the quadratic equation, the sum of whose roots is
-7
and product is
10
(i)
(
x
2
+
5
x
+
10
)
=
0
(ii)
(
x
2
+
7
x
+
10
)
=
0
(iii)
(
x
2
+
9
x
+
10
)
=
0
(iv)
(
7
x
+
10
)
=
0
(v)
(
2
x
2
+
7
x
+
10
)
=
0
Question
19
19.
Find the quadratic equation, the sum of whose roots is
4
and product is
4
(i)
(
17
x
2
−
64
x
+
64
)
=
0
(ii)
(
16
x
2
−
64
x
+
64
)
=
0
(iii)
(
16
x
2
−
61
x
+
64
)
=
0
(iv)
(
15
x
2
−
64
x
+
64
)
=
0
(v)
(
16
x
2
−
66
x
+
64
)
=
0
Question
20
20.
Find the quadratic equation, the sum of whose roots is
9
7
and product is
2
7
(i)
(
−
21
x
2
+
30
x
−
6
)
=
0
(ii)
(
−
22
x
2
+
27
x
−
6
)
=
0
(iii)
(
−
21
x
2
+
27
x
−
6
)
=
0
(iv)
(
−
20
x
2
+
27
x
−
6
)
=
0
(v)
(
−
21
x
2
+
24
x
−
6
)
=
0
Question
21
21.
If
p
and
q
are the roots of
(
x
2
−
2
x
−
3
)
=
0
,
find the equation whose roots are
p
+
1
q
and
q
+
1
p
(i)
(
3
x
2
−
2
x
−
8
)
=
0
(ii)
(
3
x
2
−
10
x
−
8
)
=
0
(iii)
(
3
x
2
−
7
x
−
6
)
=
0
(iv)
(
x
2
−
4
)
=
0
(v)
(
3
x
2
−
4
x
−
4
)
=
0
Question
22
22.
If
7
is the root of
(
x
2
+
k
x
−
28
)
=
0
, find
k
and the other root
(i)
k
=
-1
, and the other root =
-2
(ii)
k
=
-4
, and the other root =
-5
(iii)
k
=
-6
, and the other root =
-7
(iv)
k
=
-2
, and the other root =
-3
(v)
k
=
-3
, and the other root =
-4
Question
23
23.
Find the quadratic equation whose roots are
(
1
+
8
√
2
)
and
(
1
−
8
√
2
)
(i)
(
2
x
2
−
2
x
−
127
)
=
0
(ii)
(
x
2
+
x
−
127
)
=
0
(iii)
(
−
2
x
−
127
)
=
0
(iv)
(
x
2
−
2
x
−
127
)
=
0
(v)
(
x
2
−
4
x
−
127
)
=
0
Assignment Key
1) (ii)
2) (ii)
3) (v)
4) (iii)
5) (i)
6) (iv)
7) (i)
8) (iii)
9) (iv)
10) (ii)
11) (iv)
12) (iii)
13) (v)
14) (ii)
15) (v)
16) (ii)
17) (ii)
18) (ii)
19) (ii)
20) (iii)
21) (v)
22) (v)
23) (iv)
