### 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 $p\left(x\right)$ is the real number '$a$' for which $p\left(x\right)$ if $p\left(a\right)=0$. 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 $p\left(x\right)=0$.

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.

Thus, $$a=0$$ is the zero of the polynomial $$p(a)=3a$$.

2. Find the zero of a polynomial $p\left(x\right)=x-2$.

Putting $$p(x) = 0$$ in the polynomial equation.

$\begin{array}{l}0=x-2\\ \\ x=2\end{array}$

Thus $$x=2$$ is the zero of the polynomial $p\left(x\right)=x-2$.

3. For the zero polynomial, $$p(8) = 0$$, $$8$$ is the zero and it is a real number.

4. For the constant polynomial $p\left(x\right)=8$ does not have a zero.