EduSahara™ Assignment
Name : Determining Zeros of Polynomials using Graphs
Chapter : Polynomials
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Find the table of points that satisfy
the parabola equation
y
=
2
x
2
(i)
x
-2
-1
0
1
2
y
8
2
0
2
8
(ii)
x
-2
-1
0
0
2
y
8
2
0
3
8
(iii)
x
-2
-1
1
1
2
y
8
2
-1
2
8
(iv)
x
-2
-1
0
1
4
y
8
2
0
2
10
(v)
x
-2
-1
-2
1
2
y
8
2
-2
2
8
Question
2
2.
Find the table of points that satisfy
the parabola equation
y
=
(
−
2
x
2
)
(i)
x
-2
-1
-2
1
2
y
-8
-2
-2
-2
-8
(ii)
x
-2
-1
1
1
2
y
-8
-2
-1
-2
-8
(iii)
x
-2
-1
0
0
2
y
-8
-2
0
-1
-8
(iv)
x
-2
-1
0
1
4
y
-8
-2
0
-2
-6
(v)
x
-2
-1
0
1
2
y
-8
-2
0
-2
-8
Question
3
3.
Find the table of points that satisfy
the parabola equation
y
=
(
2
x
2
+
9
x
+
10
)
(i)
x
-2
-1
1
1
2
y
0
3
9
21
36
(ii)
x
-2
-1
-2
1
2
y
0
3
8
21
36
(iii)
x
-2
-1
0
1
2
y
0
3
10
21
36
(iv)
x
-2
-1
0
1
4
y
0
3
10
21
38
(v)
x
-2
-1
0
0
2
y
0
3
10
22
36
Question
4
4.
Find the table of points that satisfy
the parabola equation
y
=
(
−
4
x
2
−
8
x
−
4
)
(i)
x
-2
-1
0
0
2
y
-4
0
-4
-15
-36
(ii)
x
-2
-1
-2
1
2
y
-4
0
-6
-16
-36
(iii)
x
-2
-1
0
1
2
y
-4
0
-4
-16
-36
(iv)
x
-2
-1
0
1
4
y
-4
0
-4
-16
-34
(v)
x
-2
-1
1
1
2
y
-4
0
-5
-16
-36
Question
5
5.
Find the table of points that satisfy
the parabola equation
y
=
x
2
(i)
x
-2
-1
0
1
4
y
4
1
0
1
6
(ii)
x
-2
-1
1
1
2
y
4
1
-1
1
4
(iii)
x
-2
-1
0
0
2
y
4
1
0
2
4
(iv)
x
-2
-1
-2
1
2
y
4
1
-2
1
4
(v)
x
-2
-1
0
1
2
y
4
1
0
1
4
Question
6
6.
Find the table of points that satisfy
the parabola equation
y
=
(
−
3
x
2
)
(i)
x
-2
-1
1
1
2
y
-12
-3
-1
-3
-12
(ii)
x
-2
-1
0
1
4
y
-12
-3
0
-3
-10
(iii)
x
-2
-1
0
0
2
y
-12
-3
0
-2
-12
(iv)
x
-2
-1
0
1
2
y
-12
-3
0
-3
-12
(v)
x
-2
-1
-2
1
2
y
-12
-3
-2
-3
-12
Question
7
7.
Find the table of points that satisfy
the parabola equation
y
=
(
4
x
2
+
8
x
+
3
)
(i)
x
-2
-1
-2
1
2
y
3
-1
1
15
35
(ii)
x
-2
-1
1
1
2
y
3
-1
2
15
35
(iii)
x
-2
-1
0
1
4
y
3
-1
3
15
37
(iv)
x
-2
-1
0
0
2
y
3
-1
3
16
35
(v)
x
-2
-1
0
1
2
y
3
-1
3
15
35
Question
8
8.
Find the table of points that satisfy
the parabola equation
y
=
(
x
2
+
x
−
6
)
(i)
x
-2
-1
1
1
2
y
-4
-6
-7
-4
0
(ii)
x
-2
-1
0
0
2
y
-4
-6
-6
-3
0
(iii)
x
-2
-1
0
1
2
y
-4
-6
-6
-4
0
(iv)
x
-2
-1
-2
1
2
y
-4
-6
-8
-4
0
(v)
x
-2
-1
0
1
4
y
-4
-6
-6
-4
2
Question
9
9.
Find the roots of the quadratic equation
(
x
2
+
6
x
+
9
)
=
0
(i)
(
-2
,
-2
)
(ii)
(
-2
,
-3
)
(iii)
no real roots
(iv)
(
0
,
-3
)
(v)
(
-3
,
-3
)
Question
10
10.
Find the roots of the quadratic equation
(
x
2
−
3
x
+
2
)
=
0
(i)
(
3
,
2
)
(ii)
no real roots
(iii)
(
6
,
1
)
(iv)
(
2
,
1
)
(v)
(
3
,
1
)
Question
11
11.
Find the roots of the quadratic equation
(
−
7
x
2
−
2
x
−
1
)
=
0
(i)
(
1
,
0
)
(ii)
(
4
,
0
)
(iii)
(
1
,
1
)
(iv)
no real roots
Question
12
12.
Which of the displayed parabolae represent
the equation
y
=
2
x
2
(i)
parabola with point
K
(ii)
parabola with point
J
(iii)
parabola with point
L
(iv)
parabola with point
I
Question
13
13.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
36
16
4
0
4
16
36
(i)
y
=
2
x
2
(ii)
y
=
3
x
2
(iii)
y
=
4
x
2
(iv)
y
=
5
x
2
(v)
y
=
7
x
2
Question
14
14.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
-27
-12
-3
0
-3
-12
-27
(i)
y
=
(
−
2
x
2
)
(ii)
y
=
(
−
4
x
2
)
(iii)
y
=
(
−
6
x
2
)
(iv)
y
=
(
−
3
x
2
)
(v)
y
=
(
−
x
2
)
Question
15
15.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
5
0
-1
2
9
20
35
(i)
y
=
(
2
x
2
+
7
x
+
2
)
(ii)
y
=
(
x
2
+
5
x
+
2
)
(iii)
y
=
(
2
x
2
+
2
x
+
2
)
(iv)
y
=
(
2
x
2
+
5
x
+
2
)
(v)
y
=
(
3
x
2
+
5
x
+
2
)
Question
16
16.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
-3
0
-1
-6
-15
-28
-45
(i)
y
=
(
−
2
x
2
−
9
x
−
6
)
(ii)
y
=
(
−
2
x
2
−
7
x
−
6
)
(iii)
y
=
(
−
2
x
2
−
5
x
−
6
)
(iv)
y
=
(
−
3
x
2
−
7
x
−
6
)
(v)
y
=
(
−
x
2
−
7
x
−
6
)
Question
17
17.
Which of the displayed parabolae represents
the equation
y
=
(
x
2
−
49
9
)
(i)
parabola with point
I
(ii)
parabola with point
H
(iii)
parabola with point
J
(iv)
parabola with point
K
Question
18
18.
Which of the displayed parabolae represents
the equation
y
=
(
x
2
+
14
x
+
49
)
(i)
parabola with point
N
(ii)
parabola with point
P
(iii)
parabola with point
O
(iv)
parabola with point
Q
Question
19
19.
Which of the following are true?
a)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
always croses the X-axis
b)
The curve of a parabola
is a
curve
c)
The curve of a parabola
is a
circle
d)
The curve of a parabola
lie in only one quadrant
e)
The curve of a parabola
is a closed figure
f)
The curve of a parabola
is a
straight line
(i)
{b}
(ii)
{f,b}
(iii)
{d,e,b}
(iv)
{c,b}
(v)
{a,b}
Question
20
20.
Which of the following are true for m > 0 and a > 0?
a)
The curve of a parabola
x
=
−
m
y
2
lies in the II & III quadrant
b)
The curve of a parabola
x
=
−
m
y
2
lies in the I & II quadrant
c)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
lies in the I & II quadrant
d)
The curve of a parabola
y
=
−
m
x
2
lies in the I & II quadrant
e)
The curve of a parabola
y
=
m
x
2
lies in the I & II quadrant
(i)
{c,e,a}
(ii)
{a,e}
(iii)
{c,e}
(iv)
{b,a}
(v)
{d,b,a}
Question
21
21.
Which of the following are true for the parabola
y
=
a
x
2
+
b
x
+
c
?
a)
If the curve does not meet the X-axis ,
b
2
−
4
a
c
< 0
b)
If the curve meets the X-axis at two places, there are two distinct non-real roots.
c)
If the curve does not meet the X-axis,
there are no real roots for
y
=
a
x
2
+
b
x
+
c
d)
If the curve meets the X-axis at only one point ,
b
2
−
4
a
c
>
0
e)
If the curve meets the X-axis at only one point ,
b
2
−
4
a
c
=
0
(i)
{b,a}
(ii)
{b,a,c}
(iii)
{d,c}
(iv)
{a,c,e}
(v)
{b,d,e}
Question
22
22.
From the graph, find the approximate values of '
x
' for which
y
=
4
(i)
2.50
,
-2.50
(ii)
3.00
,
-3.00
(iii)
2.00
,
-2.00
(iv)
1.50
,
-1.50
(v)
1.00
,
-1.00
Question
23
23.
From the graph, find the approximate values of '
x
' for which
y
=
-2
(i)
-1.71
,
1.71
(ii)
-0.21
,
0.21
(iii)
0.29
,
-0.29
(iv)
-1.21
,
1.21
(v)
-0.71
,
0.71
Question
24
24.
From the graph, find the approximate values of '
x
' for which
y
=
2
(i)
-1.65
,
-3.85
(ii)
-0.15
,
-5.35
(iii)
-1.15
,
-4.35
(iv)
-0.65
,
-4.85
(v)
-2.15
,
-3.35
Question
25
25.
From the graph, find the approximate values of '
x
' for which
y
=
6
(i)
1.73
,
-1.73
(ii)
1.23
,
-1.23
(iii)
2.23
,
-2.23
(iv)
2.73
,
-2.73
(v)
0.73
,
-0.73
Question
26
26.
Which of the following equations represents the given graph ?
(i)
y
=
x
2
(ii)
y
=
3
x
2
(iii)
y
=
0
(iv)
y
=
2
x
2
(v)
y
=
(
−
x
2
)
Question
27
27.
Which of the following equations represents the given graph ?
(i)
y
=
x
2
(ii)
y
=
0
(iii)
y
=
(
−
2
x
2
)
(iv)
y
=
(
−
4
x
2
)
(v)
y
=
(
−
x
2
)
Question
28
28.
Which of the following equations represents the given graph ?
(i)
y
=
(
2
x
2
+
3
x
+
2
)
(ii)
y
=
(
2
x
2
+
5
x
+
2
)
(iii)
y
=
(
2
x
2
+
7
x
+
2
)
(iv)
y
=
(
x
2
+
5
x
+
2
)
(v)
y
=
(
3
x
2
+
5
x
+
2
)
Question
29
29.
Which of the following equations represents the given graph ?
(i)
y
=
(
−
2
x
2
−
8
x
−
2
)
(ii)
y
=
(
−
2
x
2
−
5
x
−
2
)
(iii)
y
=
(
−
2
x
2
−
2
x
−
2
)
(iv)
y
=
(
−
3
x
2
−
5
x
−
2
)
(v)
y
=
(
−
x
2
−
5
x
−
2
)
Question
30
30.
The point
(
1
,
4
)
lies on which of the given parabolae?
(i)
y
=
(
4
x
2
+
2
x
)
(ii)
y
=
(
4
x
2
+
2
x
+
4
)
(iii)
y
=
4
x
2
(iv)
y
=
(
4
x
2
+
4
)
Question
31
31.
From the following graph of
y = p(x)
, find the roots of
p(x)
(i)
4, -2 and 0
(ii)
-4, -2 and 0
(iii)
-4, 3 and 0
(iv)
-4, 4 and -6
(v)
-4, -2 and 6
Question
32
32.
From the following graph of
y = p(x)
, find the roots of
p(x)
(i)
1, 2, 4 and 5
(ii)
-3, 2, 4 and 5
(iii)
1, -4, 4 and 5
(iv)
1, 2, -2 and 5
(v)
1, 2, 4 and -7
Question
33
33.
From the following graph of
y = p(x)
, find the number of zeroes of
p(x)
(i)
2
(ii)
4
(iii)
(-1)
(iv)
1
(v)
3
Question
34
34.
From the following graph of
y = p(x)
, find the roots of
p(x)
(i)
-1, -3 and -2
(ii)
-6, 7 and -2
(iii)
-6, -3 and 4
(iv)
-6, -1 and 2
(v)
-6, -3 and -2
Question
35
35.
From the following graph of
y = p(x)
, find the roots of
p(x)
(i)
-3, 5, 0 and 1
(ii)
-3, -2, 0 and 1
(iii)
-3, -2, -5 and 1
(iv)
8, -2, 0 and 1
(v)
-3, -2, 0 and -4
Question
36
36.
From the following graph of
y = p(x)
, find the number of zeroes of
p(x)
(i)
5
(ii)
2
(iii)
1
(iv)
0
(v)
3
Question
37
37.
From the following graph of
y = p(x)
, find the roots of
p(x)
(i)
1, 2 and 3
(ii)
1, -6 and -8
(iii)
1, -3 and 4
(iv)
1, 2 and 4
(v)
-6, 2 and 4
Question
38
38.
From the following graph of
y = p(x)
, find the roots of
p(x)
(i)
3, -3, -2 and 0
(ii)
-5, -3, -2 and 0
(iii)
-5, 6, -2 and 0
(iv)
-5, -3, -4 and 0
(v)
-5, -3, -2 and 4
Question
39
39.
From the following graph of
y = p(x)
, find the number of zeroes of
p(x)
(i)
(-1)
(ii)
2
(iii)
3
(iv)
0
(v)
1
Assignment Key
1) (i)
2) (v)
3) (iii)
4) (iii)
5) (v)
6) (iv)
7) (v)
8) (iii)
9) (v)
10) (iv)
11) (iv)
12) (ii)
13) (iii)
14) (iv)
15) (iv)
16) (ii)
17) (iii)
18) (i)
19) (i)
20) (ii)
21) (iv)
22) (iii)
23) (v)
24) (iii)
25) (i)
26) (i)
27) (v)
28) (ii)
29) (ii)
30) (iii)
31) (ii)
32) (i)
33) (i)
34) (v)
35) (ii)
36) (ii)
37) (iv)
38) (ii)
39) (v)
