Dtyjlui

-5 0 $begingroup$ How can it be that the zero polynomial ( $f(x)=0$ ) is the only polynomial which has an infinite number of roots? As stated on wikipedia: The polynomial $0$ , which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero. Rather the degree of the zero polynomial is either left explicitly undefined, or defined as negative (either $−1$ or $−∞$ ). These conventions are useful when defining Euclidean division of polynomials. The zero polynomial is also unique in that it is the only polynomial having an infinite number of roots. The graph of the zero polynomial, $f(x) = 0$ , is the $x$ -axis. We can have the polynomial $x-y$ to have infinitely many roots: $x=y=text{all real numbers}$ . Where is my misunderstanding?