Theory:

Zero of polynomial \(p(x)\) is a real number '\(a\)' such that \(p(a)= 0\).
For polynomial \(p(x)\), if \(p(a) = 0\) then the zero of the polynomial is \(x = a\).
 
So, we put \(p(x) = 0\) to find zero of the polynomial.
 
The value of \(x\) is then found.
 
Important!
1. Zero of a polynomial: To find the zero of polynomial, we put \(p(x) =\) \(0\) in the given polynomial \(p(x)\).
 
2. Zeros of a polynomial p(x) is the real number 'a' for which p(x) if p(a)=0. In this situation, we say \(p(x) = 0\) is a polynomial equation, and a is a root of the polynomial.
 
3. Each real number is a zero of the zero polynomial p(x)=0.
 
4. The non-zero constant polynomial does not have zeros.
Example:
1. Find the zero of the polynomial \(p(x)=3a\).
 
Putting \(p(x) = 0\) in the polynomial equation.
 
0 = 3a.0/3 =a0=a
 
Thus, \(a=0\) is the zero of the polynomial \(p(a)=3a\).
 
 
2. Find the zero of a polynomial p(x)=x2.
 
Putting \(p(x) = 0\) in the polynomial equation.
 
0=x2x=2
 
Thus \(x=2\) is the zero of the polynomial p(x)=x2.
 
 
3. For the zero polynomial, \(p(8) = 0\), \(8\) is the zero and it is a real number.
 
 
4. For the constant polynomial p(x)=8 does not have a zero.