Zeroes of a Polynomial is defined as a number $c$ such that the value of the polynomial is zero.
i.e $p(c) = 0$
example : Consider a polynomial $p(x) = 5x^2-3x+7 $
What are the values of polynomials at $x=1$ .
Put $x=1$ in the polynomial $p(x) = 5x^2-3x+7 $
i.e $p(x) = 5x^2-3x+7 $ => $p(1) = 5(1)^2-3(1)+7 $
=> 5-3+7
=> 9
So the value of polynomial at $x=1$ is 9 .
So there can be cases when the value of the polynomial is zero . i.e $p(x) = 0$ .
Consider a polynomial $x^2-3x+2$
$p(x) = x^2-3x+2 $
equate $p(x)=0$
$x^2-3x+2 = 0$
$x^2-2x-1x+2 =0$
$x(x-2)-1(x-2) = 0$
$(x-2)(x-1) = 0$
$x=2 $ or 1
Therefore the zeros of the polynomial is 2 or 1 i.e $p(2) = 0 $ or $p(1)=0$
General formula of linear polynomial is $p(x) = ax+b$ . Since we know that zeroes of a polynomial is $p(x)=0$. Hence $ax=b = 0 $.
=> $x=-{b/a}$ .
Hence a linear polynomial has one and only one zero.

General formula of quadratic polynomial is $ax^2+bx+c$ . So the zeroes of a quadratic polynomial is $ax^2+bx+c = 0$
$x = {-b ± √ {b^2-4ac}}/{2a}$

Hence a quadratic polynomial has atmost 2 zeroes .