Find the number of zeroes in the following polynomial. 
y = x3.

We have following table

X

1

–1

0

-2

y

1

–1

0

8

 

Graph of y = x3 cuts the x-axis at one point (0, 0), so the given polynomial has one zero.

We have following table
X


1


–1


0


-2


y


1


–1


0


8
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Represent the zeroes of the quadratic polynomial x2 – 8x +12 graphically.

Let y = x2 – 8x + 12 We have following table for the given polynomial

x

1

2

3

4

5

6

7

v

5

0

-3

–4

-3

0

5

 

The graph of the equations y = x2 – 8x + 12 is are upward parabola, which is intersects the x-axis in two points (2, 0) and (6, 0)
Therefore, the given polynomial was two zeroes.

Let y = x2 – 8x + 12 We have following table for the given polynom



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Find the number of zeroes in the following linear polynomial of graphically.
2x – 7


Let y = 2x – 7
We have following table for the given polynomial


Let y = 2x – 7We have following table for the given polynomialGraphGraph of y = 2x – 7. cuts the x-axis at the point
open parentheses 7 over 2 comma 0 close parentheses

So, the given polynomial has one zero.

Let y = 2x – 7We have following table for the given polynomialGraph


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Write the nature of the graph for a linear polynomial at type ax + b, a ≠ 0.

Solution not provided.
Ans. (i) The curve (graph) is always a straight line.  
        (ii) The number of zeroes is almost one. 


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Find the number of zeroes in the following cubic polynomials graphically.
x3 – 9x.

Let = x3 – 9x
We have following table for the given polynomial

x

0

2

3

-3

1

y

0

-10

0

0

-8

 
Graph of y = x3 – 9x, cuts the x-axis at three points (0, 0), (3, 0) and (-3. 0). So, the given polynomial has three zeroes.

Let = x3 – 9xWe have following table for the given polynomial

x
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