Give examples to justify the following statement :

a) A zero of a polynomial need not be 0.

b) O may be a zero of a polynomial.

c) Every linear polynomial has one and only one zero.

d) A polynomial can have more than one zero.

Answer :

a ) A zero of a polynomial need not be 0. 

that statement is right , because  polynomial can have different zeros that can be zero or apart from that .
Example : we have a polynomial 
f( x ) = 2x³ + 5x² - 3x 
we can write it As: x( 2x² + 5x - 3 )
Equate equal to zero , we get
x( 2x² + 5x - 3 ) = 0

 2x² + 5x - 3 = 0 
using splitting middle term method and get
2x² + 6x - x - 3 = 0
2x ( x + 3 ) - 1 ( x + 3 )
(2x - 1 ) ( x + 3 ) = 0

So here zeros will be 
x = 0 , - 3 , $\frac{1}{2}$

here we can see that our polynomial have different zeros .

b ) ​0 may be a zero of a polynomial.

yes that can be posible , lets take an example :
we have a polynomial 
f( x ) = 2x³ + 5x² - 3x 

So we check for x  = 0 

f( x ) = 2 ( 0 ) + 5 ( 0 ) - 3 ( 0 ) 

f(x) = 0
Hence 0 is a zeros of polynomial 2x³ + 5x² - 3x 

c ) ​Every linear polynomial has one and only one zero. 

We know linear polynomial As y = a x  + b 
So,
Let a linear polynomial y = 2x - 4 
Then
2x - 4 = 0 

x = 2  ( Single root ) 
Hence
We can say that statement is true " ​Every linear polynomial has one and only one zero. "


d ) ​A polynomial can have more than one zero. 

Let we have a polynomial x² -2x - 3  .
We can find out its zeros by using splitting the middle term method As :

x² - 3x + x - 3 

x(x - 3 ) + 1 ( x - 3 ) 
(x + 1 ) ( x - 3 )
So,
Zeros are -1 and 3 
So we can say that statement is true " ​A polynomial can have more than one zero. "